Dissipation-Induced Instability Phenomena in Infinite-Dimensional Systems (2009)
Krechetnikov, Rouslan, Marsden, Jerrold E.
This paper develops a rigorous notion of dissipation-induced instability in infinite dimensions as an extension of the classical concept implicitly introduced by Thomson and Tait for finite degree of...
A Class of Integrable Flows on the Space of Symmetric Matrices (2009)
Bloch, Anthony M., Brînzănescu, Vasile, Iserles, Arieh, Marsden, Jerrold E., Ratiu, Tudor S.
For a given skew symmetric real n × n matrix N, the bracket [X, Y]_N = XNY − YNX defines a Lie algebra structure on the space Sym(n, N) of symmetric n × n real matrices and hence a corresponding...
Tao, Molei, Owhadi, Houman, Marsden, Jerrold E.
We introduce a new class of integrators for stiff ODEs as well as SDEs. These integrators are (i) {\it Multiscale}: they are based on flow averaging and so do not resolve the fast variables but...
Energy balance invariance for interacting particle systems (2009)
Yavari, Arash, Marsden, Jerrold E.
This paper studies the principle of invariance of balance of energy and its consequences for a system of interacting particles under groups of transformations. Balance of energy and its invariance is...
Quasivelocities and symmetries in non-holonomic systems (2009)
Bloch, Anthony M., Marsden, Jerrold E., Zenkov, Dmitry V.
This article is concerned with the theory of quasivelocities for non-holonomic systems. The equations of non-holonomic mechanics are derived using the Lagrange-d'Alembert principle written in an...
Yanao, Tomohiro, Koon, Wang Sang, Marsden, Jerrold E.
This paper uncovers novel and specific dynamical mechanisms that initiate large-amplitude collective motions in polyatomic molecules. These mechanisms are understood in terms of intramolecular energy...
Bou-Rabee, Nawaf, Marsden, Jerrold E.
In this paper, structure-preserving time-integrators for rigid body-type mechanical systems are derived from a discrete Hamilton–Pontryagin variational principle. From this principle, one can...
Lagrangian coherent structures in the planar elliptic restricted three-body problem (2009)
Gawlik, Evan S., Marsden, Jerrold E., Du Toit, Philip, Campagnola, Stefano
This study investigates Lagrangian coherent structures (LCS) in the planar elliptic restricted three-body problem (ER3BP), a generalization of the circular restricted three-body problem (CR3BP) that...
Dirac cotangent bundle reduction (2009)
Yoshimura, Hiroaki, Marsden, Jerrold E.
The authors' recent paper in Reports in Mathematical Physics develops Dirac reduction for cotangent bundles of Lie groups, which is called Lie--Dirac reduction . This procedure simultaneously...
Jerrold E. Marsden, Steve Shkoller, Communicated S. Müller
The purpose of this paper is twofold. First, we give a derivation of the Lagrangian averaged Euler (LAE-α) and Navier-Stokes (LANS-α) equations. This theory involves a spatial scale α and the...
DYNAMIC MODELING OF α IN THE ISOTROPIC LAGRANGIAN AVERAGED NAVIER-STOKES-α EQUATIONS (2009)
Hongwu Zhao, Kamran Mohseni, Jerrold E. Marsden
A dynamic procedure for the Lagrangian Averaged Navier-Stokes-α (LANS-α) equations is developed where the variation in the parameter α in the direction of anisotropy is determined in a...
Poisson structure and invariant manifolds on Lie groups (2009)
Jerrold E. Marsden, Sergey Pekarsky, Steve Shkoller
For a discrete mechanical system on a Lie group G determined by a (reduced) Lagrangian ℓ we define a Poisson structure via the pull-back of the Lie-Poisson structure on g ∗ by the corresponding...
1998b] The Euler-Poincaré equations in geophysical fluid dynamics (2009)
Darryl D. Holm, Jerrold E. Marsden, Tudor S. Ratiu
Recent theoretical work has developed the Hamilton’s-principle analog of Lie-Poisson Hamiltonian systems defined on semidirect products. The main theoretical results are twofold: 1....
AN ALMOST POISSON STRUCTURE FOR THE GENERALIZED RIGID BODY EQUATIONS (2009)
Anthony M. Bloch, Petere Crouch, Jerrold E. Marsden, Tudors Ratiu
Abstract: In this paper we introduce almost Poisson structures on Lie groups which generalize Poisson structures based on the use of the classical Yang-Baxter identity. Almost Poisson structures fail...
Antonio Hernández-garduño, Autónoma México, Jeffrey K. Lawson, Jerrold E. Marsden
This paper gives necessary and sufficient conditions for the (n-dimensional) generalized free rigid body to be in a state of relative equilibrium. The conditions generalize those for the case of the...
Controlled Lagrangian Systems with Gyroscopic Forcing and Dissipation (2009)
Craig Woolsey, Anthony M. Bloch, Naomi Ehrich Leonard, Chevva Konda Reddy, Dong Eui Chang, Jerrold E. Marsden
This paper describes a procedure for incorporating artificial gyroscopic forces in the method of controlled Lagrangians. These energy-conserving forces provide additional freedom to expand the basin...
The Euler Equations on Thin Domains (2009)
Jerrold E. Marsden, Tudor S. Ratiu, Geneviève Raugel
For the Euler equations in a thin domain Qε =Ω×(0,ε), Ω a rectangle in R 2, with initial data in (W 2,q (Qε)) 3, q>3, bounded uniformly in ε, the classical solution is shown to exist on a...
Tippe Top Inversion as a Dissipation-Induced Instability ∗ (2009)
Jerrold E. Marsden, Louis A. Romero
Abstract. By treating tippe top inversion as a dissipation-induced instability, we explain tippe top inversion through a system we call the modified Maxwell–Bloch equations. We revisit previous...
Time–frequency analysis of the restricted three-body
1 Symplectic and Poisson Geometry of (2009)
Wang Sang Koon, Dynamical Systems, Jerrold E. Marsden
Many important problems in multibody dynamics, the dynamics of wheeled vehicles and motion generation, involve nonholonomic mechanics. Many of these systems have symmetry, such as the group of...
Factor-analysis of nonlinear mappings: pregularity theory (2009)
(Communicated by Steve Shkoller) Ever since we began to prove things that were obviously true, many of them turned out to be false, Bertrand Russell Abstract. The paper presents recent advances in...
Covariant balance laws in continua with microstructure (2009)
Yavari, Arash, Marsden, Jerrold E.
The purpose of this paper is to extend the Green-Naghdi-Rivlin balance of energy method to continua with microstructure. The key idea is to replace the group of Galilean transformations with the...
Shadden, Shawn C., Lekien, Francois, Paduan, Jeffrey D., Chavez, Francisco P., Marsden, Jerrold E.
This paper investigates the transport structure of surface currents around the Monterey Bay, CA region. Currents measured by radar stations around Monterey Bay indicate the presence of strong,...
Lagrangian coherent structures in the planar elliptic restricted three-body problem (2009)
Gawlik, Evan S., Marsden, Jerrold E., Du Toit, Philip C., Campagnola, Stefano
This study investigates Lagrangian coherent structures (LCS) in the planar elliptic restricted three-body problem (ER3BP), a generalization of the circular restricted three-body problem (CR3BP) that...
Study of blood flow impact on growth of thrombi using a multiscale model (2009)
Xu, Zhiliang, Chen, Nan, Shadden, Shawn C., Marsden, Jerrold E., Kamocka, Malgorzata M., Rosen, Elliot D., ...
An extended multiscale model is introduced for studying the formation of platelet thrombi in blood vessels. The model describes the interplay between viscous, incompressible blood plasma, activated...
Geometric Foundations of Motion and Control (2008)
Some interesting aspects of motion and control such as those found in biological and robotic locomotion, and attitude control of spacecraft, involve geometric concepts. When an animal or a robot...
Eitan Grinspun (columbia, Jerrold E. Marsden, Yiying Tong
Variational Integrators [Marsden and West (2001)] approximate the Lagrangian of a mechanical system, then use a variational principle to derive a structure-preserving numerical scheme. However, as...
Flat nonholonomic matching (2008)
Dmitry V. Zenkov, Anthony M. Bloch, Jerrold E. Marsden
In this paper we extend the matching technique to a class of nonholonomic systems with symmetries. Assuming that the momentum equation defines an integrable distribution, we introduce a family of...
Formation Flight Near Libration Points: Survey and Recommendations (2008)
Martin W. Lo, Wang Sang Koon, Jerrold E. Marsden, Richard M. Murray
This paper gives a survey of some of the issues involved in formation flight of satellites near a halo orbit. An example of the use of such a formation is to act as a telescope for imaging...
Dong Eui Chang, Jerrold E. Marsden
Dedicated to Klaus Kirchgässner on the occasion of his 70th birthday Abstract. We derive the classical Delaunay variables by finding a suitable symmetry action of the three torus T 3 on the phase...
Feedback Stabilization of Relative Equilibria for Mechanical Systems with Symmetry (2008)
Anthony M. Bloch, Jerrold E. Marsden
This paper is an outgrowth of the work of Bloch, Krishnaprasad, Marsden and Sánchez de Alvarez [1992], where a feedback control that stabilizes intermediate axis rigid body rotation using an...
Atlantis, Paradise Island, Bahamas Uncertainty in the Dynamics of Conservative Maps (2008)
Oliver Junge, Jerrold E. Marsden
Abstract — This paper studies the effect of uncertainty, using random perturbations, on area preserving maps of R 2 to itself. We focus on the standard map and a discrete Duffing oscillator as...
ACC99-IEEE0267 Model reduction for analysis of cascading failures in power systems (2008)
Pablo A. Parrilo, Sanjay Lall, Fernando Paganini, George C. Verghese, Bernard C. Lesieutre, Jerrold E. Marsden
In this paper, we apply a principal-orthogonal decomposition based method to the model reduction of a hybrid, nonlinear model of a power network. The results demonstrate that the sequence of fault...
Mathematik und Physik ZAMP On the geometric character of stress in continuum mechanics (2008)
Eva Kanso, Marino Arroyo, Yiying Tong, Arash Yavari, Jerrold E. Marsden, Mathieu Desbrun
Abstract. This paper shows that the stress field in the classical theory of continuum mechanics may be taken to be a covector-valued differential two-form. The balance laws and other fundamental laws...
Wang Sang Koon, Martin W. Lo, Jerrold E. Marsden, Shane D. Ross
In 1991, the Japanese Hiten mission used a low energy transfer with a ballistic capture at the Moon which required less ∆V than a standard Hohmann transfer to the Moon. In this paper, we apply the...
Reduced-dimension Models in Nonlinear Finite Element Dynamics of Continuous Media (2008)
Petr Krysl, Sanjay Lall, Jerrold E. Marsden
Model reduction is a means of arriving at simplified dynamical descriptions of the behavior of a complex system that may be hard to model directly. Instead of attempting to model the overall behavior...
Time-frequency analysis of the restricted three body problem 2
Optimal reconfiguration of formation flying spacecraft - a decentralized approach (2008)
Oliver Junge, Jerrold E. Marsden, Sina Ober-blöbaum
Abstract — This paper introduces a hierarchical, decentralized, and parallelizable method for dealing with optimization problems with many agents. It is theoretically based on a hierarchical...
REDUCTION OF CONTROLLED LAGRANGIAN AND HAMILTONIAN SYSTEMS WITH SYMMETRY ∗ (2008)
Abstract. We develop reduction theory for controlled Lagrangian and controlled Hamiltonian systems with symmetry. Reduction theory for these systems is needed in a variety of examples, such as a...
New Methods in Celestial Mechanics and Mission Design (2008)
Jerrold E. Marsden, D. Ross, Katalin Grubits, Oliver Junge, Wang-sang Koon, ...
To Henri Poincaré on the 150th anniversary of his birth. Abstract. The title of this paper is inspired by the work of Poincaré [1890, 1892], who introduced many key dynamical systems methods during...
AN OVERVIEW OF VARIATIONAL INTEGRATORS (2008)
Adrian Lew, Jerrold E. Marsden, Michael Ortiz, Matthew West
Tom Hughes has been a friend, collaborator, and colleague to some of us for several decades and has been a major inspiration on many fronts. One aspect of his personality that is held most dear is...
Controlled Lagrangians and Potential Shaping for Stabilization of Discrete Mechanical Systems (2008)
Anthony M. Bloch, Jerrold E. Marsden
Abstract — The method of controlled Lagrangians for discrete mechanical systems is extended to include potential shaping in order to achieve complete state-space asymptotic stabilization. New terms...
Frederic Gabern, Wang S. Koon, Jerrold E. Marsden
This paper studies the dynamics of a spacecraft moving in the field of a binary asteroid. The asteroid pair is modeled as a rigid body and a sphere moving in a plane, while the spacecraft moves in...
INSTITUTE OF PHYSICS PUBLISHING NONLINEARITY (2008)
Clarence W Rowley, Ioannis G Kevrekidis, Jerrold E Marsden, Kurt Lust
Reduction and reconstruction for self-similar
Matching and Stabilization by the Method of Controlled (2008)
Anthony M. Bloch, Naomi Ehrich Leonard, Jerrold E. Marsden
3
Short Running Title: Dynamic Polar Decomposition and Inversion (2008)
Neil H. Getz, Jerrold E. Marsden
We show howonemay obtain polar decomposition as well as inversion of xed and time-varying matrices using a class of nonlinear continuous-time dynamical systems. First we construct a dy-namic system...
Covariant Balance Laws in Continua with Microstructure (2008)
Yavari, Arash, Marsden, Jerrold E.
The purpose of this paper is to extend the Green-Naghdi-Rivlin balance of energy method to continua with microstructure. The key idea is to replace the group of Galilean transformations with the...
The Geometry and Dynamics of Interacting Rigid Bodies and Point Vortices (2008)
Vankerschaver, Joris, Kanso, Eva, Marsden, Jerrold E.
We derive the equations of motion for a planar rigid body of circular shape moving in a 2D perfect fluid with point vortices using symplectic reduction by stages. After formulating the theory as a...
Variational integrators for constrained dynamical systems (2008)
Leyendecker, Sigrid, Marsden, Jerrold E., Ortiz, Michael
A variational formulation of constrained dynamics is presented in the continuous and in the discrete setting. The existing theory on variational integration of constrained problems is extended by...
2001], Variational methods, multisymplectic geometry and continuum mechanics (2008)
Jerrold E. Marsden, Sergey Pekarsky, Matthew West, Steve Shkoller
This paper presents a variational and multisymplectic formulation of both compressible and incompressible models of continuum mechanics on general Riemannian manifolds. A general formalism is...
The Geometry of Peaked Solitons and Billiard Solutions of a Class of Integrable PDE’s ∗ (2008)
Darryl D. Holm, Jerrold E. Marsden
The purpose of this letter is to investigate the geometry of new classes of solitonlike solutions for integrable nonlinear equations. One example is the class of peakons introduced by Camassa and...
Dong Eui Chang, David F. Chichka, Jerrold E. Marsden
Abstract. We present a study of the transfer of satellites between elliptic Keplerian orbits using Lyapunov stability theory specific to this problem. The construction of Lyapunov functions is based...
2003], The Lie-Poisson structure of the Euler equations of an ideal fluid. (preprint (2008)
Sergiy Vasylkevych, Jerrold E. Marsden
Abstract. This paper provides a precise sense in which the time t map for the Euler equations of an ideal fluid in a region in R n (or a smooth compact n-manifold with boundary) is a Poisson map...
Mechanical Integrators Derived from a Discrete Variational Principle (2008)
Je�rey M. Wendl, Jerrold E. Marsden
Many numerical integrators for mechanical system simulation are created by using discrete algorithms to approximate the continuous equations of motion. In this paper � we present a procedure to...
MATCHING AND STABILIZATION OFTHEUNICYCLEWITHRIDER (2008)
Dmitry V. Zenkov, Anthony M. Bloch, Naomi E. Leonard, Jerrold E. Marsden
Abstract: In this paper we apply matching techniques for controlled Lagrangians to the stabilization problem of a nonholonomic system consisting of a unicycle with rider. We show how generalized...
Anthony M. Bloch, Naomi Ehrich Leonard, Jerrold E. Marsden
In this paper we develop a constructive approach to the determination of stabilizing control laws for a class of Lagrangian mechanical systems with symmetry * systems whose underlying dynamics are...
A resolution of the transition to turbulence paradox (2008)
Krechetnikov, Rouslan, Marsden, Jerrold E.
Understanding the transition to turbulence has been impeded by a modeling oversight
Dissipation-Induced Heteroclinic Orbits in Tippe Tops (2008)
Bou-Rabee, Nawaf M., Marsden, Jerrold E., Romero, Louis A.
This paper demonstrates that the conditions for the existence of a dissipation-induced heteroclinic orbit between the inverted and noninverted states of a tippe top are determined by a complex...
Variational Integrators for Maxwell's Equations with Sources (2008)
Stern, Ari, Tong, Yiying, Desbrun, Mathieu, Marsden, Jerrold E.
In recent years, two important techniques for geometric numerical discretization have been developed. In computational electromagnetics, spatial discretization has been improved by the use of mixed...
2000] Reduction of Hamilton's Variational Principle, Dyn (2008)
Sameer M. Jalnapurkar, Jerrold E. Marsden
This paper builds on the initial work of Marsden and Scheurle on nonabelian Routh reduction. The main objective of the present paper is to carry out the reduction of variational principles in further...
A MATHEMATICAL MODEL OF TRUE POLAR WANDER (2008)
Melvin Boon-tiong, Mentor Prof, Jerrold E. Marsden
Abstract. Inertial Interchange True Polar Wander has been suggested as a possible mechanism for the rapid continental drift during the early Cambrian era. The signi…cant separation of time scales...
Bou-Rabee, Nawaf, Marsden, Jerrold E.
In this paper structure-preserving time-integrators for rigid body-type mechanical systems are derived from a discrete Hamilton-Pontryagin variational principle. From this principle one can derive a...
Parametrization and stress–energy–momentum tensors in metric field theories (2008)
Castrillón López, Marco, Gotay, Mark J., Marsden, Jerrold E.
We give an exposition of the 1972 parametrization method of Kuchař in the context of the multisymplectic approach to field theory. The purpose of the formalism developed here is to make any...
Parametrization and Stress-Energy-Momentum Tensors in Metric Field Theories (2007)
Lopez, Marco Castrillon, Gotay, Mark J., Marsden, Jerrold E.
We give an exposition of the parametrization method of Kuchar [1973] in the context of the multisymplectic approach to field theory, as presented in Gotay and Marsden [2008a]. The purpose of the...
The Lie-Poisson Structure of the Euler Equations of an Ideal Fluid (2007)
Vasylkevych, Sergiy, Marsden, Jerrold E.
This paper provides a precise sense in which the time t map for the Euler equations of an ideal fluid in a region in R^n (or a smooth compact n-manifold with boundary) is a Poisson map relative to...
Concatenating Variational Principles and the Kinetic Stress-Energy-Momentum Tensor (2007)
Lopez, Marco Castrillon, Gotay, Mark J., Marsden, Jerrold E.
We show how to "concatenate" variational principles over different bases into one over a single base, thereby providing a unified Lagrangian treatment of interacting systems. As an example we study a...
James R. Arvo, Jerrold E. Marsden, Anil N. Hirani, Anil N. Hirani
I'd like to thank my advisors Prof. Jerrold E. Marsden and Prof. Jim Arvo for their invaluable help and advice. The comments made by the members of my candidacy committee were also very helpful....
Reduction of Hamilton's Variational Principle (2007)
Sameer M. Jalnapurkar, Jerrold E. Marsden
This paper builds on the initial work of Marsden and Scheurle on nonabelian Routh reduction. The main objective of the present paper is to carry out the reduction of variational principles in further...
John F. Canny, Jerrold E. Marsden, Linda G. Bushnell, Linda G. Bushnell
.9> IBM T. J. Watson Research Center, Summer Intern. Advanced Robotics Department of Manufacturing Research, Yorktown Heights, New York. Analysis and simulation of Sawyer linear step motors. 1991....
1998b] The Euler-Poincaré equations in geophysical fluid dynamics (2007)
Darryld. Holm, Jerrold E. Marsden, Tudor S. Ratiu
Recent theoretical work has developed the Hamilton’s-principle analog of Lie-Poisson Hamiltonian systems defined on semidirect products. The main theoretical results are twofold: 1....
Mark S. Alber, Roberto Camassa, Yuri N. Fedorov, Darryl D. Holm, Jerrold E. Marsden
extension of the algebraic-geometric method for nonlinear integrable PDE’s is shown to lead to new piecewise smooth weak solutions of a class of Ncomponent systems of nonlinear evolution equations....
James R. Arvo, Jerrold E. Marsden, Anil N. Hirani, Anil N. Hirani
I'd like to thank my advisors Prof. Jerrold E. Marsden and Prof. Jim Arvo for their invaluable help and advice. The comments made by the members of my candidacy committee were also very helpful....
2001], Variational methods, multisymplectic geometry and continuum mechanics (2007)
Jerrold E. Marsden, Sergey Pekarsky, Steve Shkoller
This paper presents a variational and multisymplectic formulation of both compressible and incompressible models of continuum mechanics on general Riemannian manifolds. A general formalism is...
Jeffrey M. Wendlandt, Jerrold E. Marsden
Many numerical integrators for mechanical system simulation are created by using discrete algorithms to approximate the continuous equations of motion. In this paper, we present a procedure to...
Pablo A. Parrilo, Sanjay Lall, George C. Verghese, Bernard C. Lesieutre, Jerrold E. Marsden
analysis of cascading failure for power networks
Momentum Maps and Classical Fields Part I: Covariant Field Theory (2007)
Classical Fields Part, Mark J. Gotay, James Isenberg, Richard Montgomery, Jerrold E. Marsden
this paper.) In Part I we develop some of the basic theory of classical fields from a spacetime covariant viewpoint. Throughout we restrict attention to first order theories; these are theories whose...
Computational Electromagnetism with Variational Integrators and Discrete Differential Forms (2007)
Stern, Ari, Tong, Yiying, Desbrun, Mathieu, Marsden, Jerrold E.
In this paper, we introduce a general family of variational, multisymplectic numerical methods for solving Maxwell's equations, using discrete differential forms in spacetime. In doing so, we...
Lagrangian coherent structures in n-dimensional systems (2007)
Lekien, Francois, Shadden, Shawn C., Marsden, Jerrold E.
Numerical simulations and experimental observations reveal that unsteady fluid systems can be divided into regions of qualitatively different dynamics. The key to understanding transport and stirring...
Controlled Lagrangians and Stabilization of Discrete Mechanical Systems I (2007)
Bloch, Anthony M., Leok, Melvin, Marsden, Jerrold E., Zenkov, Dmitry V.
Controlled Lagrangian and matching techniques are developed for the stabilization of relative equilibria and equilibria of discrete mechanical systems with symmetry as well as broken symmetry....
Gyration-radius dynamics in structural transitions of atomic clusters (2007)
Yanao, Tomohiro, Koon, Wang S., Marsden, Jerrold E., Kevrekidis, Ioannis G.
This paper is concerned with the structural transition dynamics of the six-atom Morse cluster with zero total angular momentum, which serves as an illustrative example of the general reaction...
Hamiltonian reduction by stages / Jerrold E. Marsden ...[et al.] (2007)
Incluye bibliografía e índice
Hamiltonian reduction by stages (2007)
Marsden, Jerrold E., Misiolek, Gerard, Ortega, Juan-Pablo, Perlmutter, Matthew, Ratiu, Tudor S.
Hamiltonian Reduction by Stages (2007)
Jerrold E. Marsden, Département De Mathématiques, Matthew Perlmutter, Tudor S. Ratiu, Marsden Jerrold
ii
Concatenating Variational Principles and the Kinetic Stress-Energy-Momentum Tensor (2007)
Marco Castrillón López, Mark J. Gotay, Jerrold E. Marsden
We show how to “concatenate ” variational principles over different bases into one over a single base, thereby providing a unified Lagrangian treatment of interacting systems. As an example we...
Parametrization and Stress-Energy-Momentum Tensors in Metric Field Theories (2007)
Marco Castrillón López, Mark J. Gotay, Jerrold E. Marsden
We give an exposition of the parametrization method of Kuchaˇr [1973] in the context of the multisymplectic approach to field theory, as presented in Gotay and Marsden [2008a]. The purpose of the...
Alexander Mckenzie, Alexander Mckenzie, Jerrold E. Marsden
iii My sincerest thanks to Mathieu Desbrun. Special thanks to research collaborators Yiying Tong,
Discrete Routh reduction (2006)
Jalnapurkar, Sameer M., Leok, Melvin, Marsden, Jerrold E., West, Matthew
This paper develops the theory of Abelian Routh reduction for discrete mechanical systems and applies it to the variational integration of mechanical systems with Abelian symmetry. The reduction of...
Discrete Routh reduction (2006)
Jalnapurkar, Sameer M, Leok, Melvin, Marsden, Jerrold E., West, Matthew
This paper develops the theory of Abelian Routh reduction for discrete mechanical systems and applies it to the variational integration of mechanical systems with Abelian symmetry. The reduction of...
Mass effects and internal space geometry in triatomic reaction dynamics (2006)
Yanao, Tomohiro, Koon, Wang S., Marsden, Jerrold E.
The effect of the distribution of mass in triatomic reaction dynamics is analyzed using the geometry of the associated internal space. Atomic masses are appropriately incorporated into internal...
Lagrangian analysis of fluid transport in empirical vortex ring flows (2006)
Shadden, Shawn C., Dabiri, John O., Marsden, Jerrold E.
In this paper we apply dynamical systems analyses and computational tools to fluid transport in empirically measured vortex ring flows. Measurements of quasisteadily propagating vortex rings...
On spatial and material covariant balance laws in elasticity (2006)
Yavari, Arash, Marsden, Jerrold E., Ortiz, Michael
This paper presents some developments related to the idea of covariance in elasticity. The geometric point of view in continuum mechanics is briefly reviewed. Building on this, regarding the...
Controlled Lagrangians and Potential Shaping for Stabilization of Discrete Mechanical Systems (2006)
Bloch, Anthony M., Leok, Melvin, Marsden, Jerrold E., Zenkov, Dmitry V.
The method of controlled Lagrangians for discrete mechanical systems is extended to include potential shaping in order to achieve complete state-space asymptotic stabilization. New terms in the...
New methods in celestial mechanics and mission design (2006)
Marsden, Jerrold E., Ross, Shane D.
The title of this paper is inspired by the work of Poincaré [1890, 1892], who introduced many key dynamical systems methods during his research on celestial mechanics and especially the three-body...
Horseshoes and Arnold Diffusion for Hamiltonian Systems on Lie Groups (2006)
Holmes, Philip J., Marsden, Jerrold E.
The Melnikov theory of perturbations of Hamiltonian systems containing homoclinic orbits is extended to systems containing canonical variables belonging to the coadjoint orbits of a Lie group. This...
Dissipation Induced Instabilities (2006)
Bloch, Anthony, Krishnaprasad, P. S., Marsden, Jerrold E., Ratiu, Tudor S.
The main goal of this paper is to prove that if the energy-momentum (or energy-Casimir) method predicts formal instability of a relative equilibrium in a Hamiltonian system with symmetry, then with...
Dirac structures and lagrangian mechanics part i: Implicit lagrangian systems (2006)
Hiroaki Yoshimura, Jerrold E. Marsden
This paper develops the notion of implicit Lagrangian systems and presents some of their basic properties in the context of Dirac structures. This setting includes degenerate Lagrangian systems and...
Dirac structures and lagrangian mechanics part i: Implicit lagrangian systems (2006)
Hiroaki Yoshimura, Jerrold E. Marsden
Part I of this paper introduced the notion of implicit Lagrangian systems and their geometric structure was explored in the context of Dirac structures. In this part, we develop the variational...
A Class of Integrable Geodesic Flows on the Symplectic Group and the Symmetric Matrices (2005)
Bloch, Anthony M., Iserles, Arieh, Marsden, Jerrold E., Ratiu, Tudor S.
This paper shows that the left-invariant geodesic flow on the symplectic group relative to the Frobenius metric is an integrable system that is not contained in the Mishchenko-Fomenko class of rigid...
A Discrete Theory of Connections on Principal Bundles (2005)
Leok, Melvin, Marsden, Jerrold E., Weinstein, Alan D.
Connections on principal bundles play a fundamental role in expressing the equations of motion for mechanical systems with symmetry in an intrinsic fashion. A discrete theory of connections on...
Discrete Exterior Calculus (2005)
Desbrun, Mathieu, Hirani, Anil N., Leok, Melvin, Marsden, Jerrold E.
We present a theory and applications of discrete exterior calculus on simplicial complexes of arbitrary finite dimension. This can be thought of as calculus on a discrete space. Our theory includes...
Discrete Routh Reduction (2005)
Jalnapurkar, Sameer M., Leok, Melvin, Marsden, Jerrold E., West, Matthew
This paper develops the theory of abelian Routh reduction for discrete mechanical systems and applies it to the variational integration of mechanical systems with abelian symmetry. The reduction of...
Transport of Mars-Crossing Asteroids from the Quasi-Hilda Region (2005)
Dellnitz, Michael, Junge, Oliver, Lo, Martin W., Marsden, Jerrold E., Padberg, Kathrin, Preis, Robert, ...
We employ set oriented methods in combination with graph partitioning algorithms to identify key dynamical regions in the Sun-Jupiter-particle three-body system. Transport rates from a region near...
Discrete Poincaré Lemma (2005)
Desbrun, Mathieu, Leok, Melvin, Marsden, Jerrold E.
This paper proves a discrete analogue of the Poincar´e lemma in the context of a discrete exterior calculus based on simplicial cochains. The proof requires the construction of a generalized cone...
Transport in dynamical astronomy and multibody problems (2005)
Dellnitz, Michael, Junge, Oliver, Koon, Wang Sang, Lekien, Francois, Lo, Martin W., Marsden, Jerrold E., ...
We combine the techniques of almost invariant sets (using tree structured box elimination and graph partitioning algorithms) with invariant manifold and lobe dynamics techniques. The result is a new...
Transport in dynamical astronomy and multibody problems (2005)
Dellnitz, Michael, Junge, Oliver, Koon, Wang Sang, Lekien, Francois, Lo, Martin W., Marsden, Jerrold E., ...
We combine the techniques of almost invariant sets (using tree structured box elimination and graph partitioning algorithms) with invariant manifold and lobe dynamics techniques. The result is a new...
Frederic Gabern, Wang S. Koon, Jerrold E. Marsden, Shane D. Ross
The computation, starting from basic principles, of chemical reaction rates in realistic systems (with three or more degrees of freedom) has been a longstanding goal of the chemistry community. Our...
1992] On the Dynamics and (2005)
Anthony M. Bloch, Jerrold E. Marsden, Dmitry V. Zenkov
Nonholonomic systems are, roughly speaking, mechanical systems with constraints on their velocity that are not derivable from position constraints. They arise, for instance, in mechanical systems
Discrete mechanics and optimal control (2005)
Oliver Junge, Jerrold E. Marsden, Sina Ober-blöbaum
Abstract: A new approach to the solution of optimal control problems for mechanical systems is proposed. It is based on a direct discretization of the Lagrange-d’Alembert principle for the system...
Transport in Dynamical Astronomy and Multibody Problems (2005)
Michael Dellnitz, Oliver Junge, Wang Sang Koon, Francois Lekien, Martin W. Lo, Jerrold E. Marsden, ...
We combine the techniques of almost invariant sets (using tree structured box elimination and graph partitioning algorithms) with invariant manifold and lobe dynamics techniques. The result is a new...
Discrete Mechanics And Optimal Control (2005)
Oliver Junge Jerrold, Jerrold E. Marsden, Sina Ober-blöbaum
A new approach to the solution of optimal control problems for mechanical systems is proposed. It is based on a direct discretization of the Lagrange-d'Alembert principle for the system (as...
Michael Dellnitz, Katalin A. Grubits, Jerrold E. Marsden, Kathrin Padberg, Bianca Thiere
We present a new method based on set oriented computations for the calculation of reaction rates in chemical systems. The method is demonstrated with the Rydberg atom, an example for which...
1992] On the Dynamics and (2005)
Anthony M. Bloch, Jerrold E. Marsden, Dmitry V. Zenkov
Nonholonomic systems are, roughly speaking, mechanical systems with constraints on their velocity that are not derivable from position constraints. They arise, for instance, in mechanical systems
Uncertainty in the dynamics of conservative maps (2004)
Junge, Oliver, Marsden, Jerrold E., Mezic, Igor
This paper studies the effect of uncertainty, using random perturbations, on area preserving maps of ℝ^2 to itself. We focus on the standard map and a discrete Duffing oscillator as specific...
Gotay, Mark J., Isenberg, James, Marsden, Jerrold E.
With the covariant formulation in hand from the first paper of this series (physics/9801019), we begin in this second paper to study the canonical (or ``instantaneous'') formulation of classical...
Reduction of Controlled Lagrangian and Hamiltonian Systems with Symmetry (2004)
Chang, Dong Eui, Marsden, Jerrold E.
We develop reduction theory for controlled Lagrangian and controlled Hamiltonian systems with symmetry. Reduction theory for these systems is needed in a variety of examples, such as a spacecraft...
A Dynamic alpha Model for the Lagrangian Averaged Navier-Stokes-alpha Equations (2004)
Zhao, Hongwu, Mohseni, Kamran, Marsden, Jerrold E.
This paper has been withdrawn by the authors for adding some results.
Vela-Arevalo, Luz V., Marsden, Jerrold E.
A method of time-frequency analysis based on wavelets is applied to the problem of transport between different regions of the solar system, using the model of the circular restricted three-body...
Controlled Lagrangian systems with gyroscopic forcing and dissipation (2004)
Woolsey, Craig, Reddy, Chevva Konda, Bloch, Anthony M., Chang, Dong Eui, Leonard, Naomi Ehrich, Marsden, Jerrold E.
This paper describes a procedure for incorporating artificial gyroscopic forces and physical dissipation in the method of controlled Lagrangians. Energy-conserving gyroscopic forces provide...
Tippe Top Inversion as a Dissipation-Induced Instability (2004)
Bou-Rabee, Nawaf M., Marsden, Jerrold E., Romero, Louis A.
By treating tippe top inversion as a dissipation-induced instability, we explain tippe top inversion through a system we call the modified Maxwell--Bloch equations. We revisit previous work done on...
Cálculo vectorial / Jerrold E. Marsden, Anthony J. Tromba (2004)
Marsden, Jerrold E., Tromba, Anthony
Traducción de: Vector calculus
A geometric treatment of Jellett’s egg (2004)
Jerrold E. Marsden, Louis A. Romero
Key words rising egg, dissipation-induced instability, Jellett momentum map, adiabatic invariants
Optimal trajectory generation in ocean flows (2004)
Tamer Inanc, Shawn C. Shadden, Jerrold E. Marsden
Abstract — In this paper it is shown that Lagrangian Coherent Structures (LCS) are useful in determining near optimal trajectories for autonomous underwater gliders in a dynamic ocean environment....
Geometric Mechanics and the Dynamics of Asteroid Pairs (2004)
Hernán Cendra, Bahia Blanca, Jerrold E. Marsden
This paper studies, using the technique of Lagrangian reduction, the geometric mechanics of a pair of asteroids in orbit about each other under mutual gravitational attraction. 1
Uncertainty in the Dynamics of Conservative Maps (2004)
Oliver Junge, Jerrold E. Marsden
This paper studies the effect of uncertainty, using random perturbations, on area preserving maps of R to itself. We focus on the standard map and a discrete Duffing oscillator as specific examples....
Holm, Darryl D., Marsden, Jerrold E.
We study the dynamics of measure-valued solutions of what we call the EPDiff equations, standing for the {\it Euler-Poincar\'e equations associated with the diffeomorphism group (of $\mathbb{R}^n$ or...
Collision avoidance for multiple agent systems (2003)
Chang, Dong Eui, Shadden, Shawn C., Marsden, Jerrold E., Olfati-Saber, Reza
Techniques using gyroscopic forces and scalar potentials are used to create swarming behaviors for multiple agent systems. The methods result in collision avoidance between the agents as well as with...
Mohseni, Kamran, Kosovic, Branko, Shkoller, Steve, Marsden, Jerrold E.
Capabilities for turbulence calculations of the Lagrangian averaged Navier-Stokes (LANS-alpha) equations are investigated in decaying and statistically stationary three-dimensional homogeneous and...
Reduction and reconstruction for self-similar dynamical systems (2003)
Rowley, Clarence W., Kevrekidis, Ioannis G., Marsden, Jerrold E., Lust, Kurt
We present a general method for analysing and numerically solving partial differential equations with self-similar solutions. The method employs ideas from symmetry reduction in geometric mechanics,...
Variational principles for Lie-Poisson and Hamilton-Poincaré equations (2003)
Cendra, Hernán, Marsden, Jerrold E., Pekarsky, Sergey, Ratiu, Tudor S.
Gyroscopic Forces and Collision Avoidance with Convex Obstacles (2003)
Dong Eui Chang, Jerrold E. Marsden
Summary. This paper introduces gyroscopic forces as an tool that can be used in addition to the use of potential forces in the study of collision and convex obstacle avoidance. It makes use of the...
Jerrold E. Marsden, T. Ratiu, Alan Weinstein, R. Schmid
The symplectic and Poisson structures on reduced phase spaces are reviewed, including the symplectic structure on coadjoint orbits of a Lie group and the Lie-Poisson structure on the dual of a Lie...
Transport in dynamical astronomy and multibody problems (2003)
Michael Dellnitz, Oliver Junge, Wang Sang Koon, Francois Lekien, Martin W. Lo, Jerrold E. Marsden, ...
We combine the techniques of almost invariant sets (using tree structured box elimination and graph partitioning algorithms) with invariant manifold and lobe dynamics techniques. The result is a new...
Discrete Exterior Calculus for Variational Problems in Computer Vision and Graphics (2003)
Mathieu Desbrun, Anil N. Hirani, Jerrold E. Marsden
This paper demonstrates how discrete exterior calculus tools may be useful in computer vision and graphics. Avariational approach provides a link with mechanics.
The symmetric representation of the rigid body equations and their discretization (2002)
Bloch, Anthony M., Crouch, Peter E, Marsden, Jerrold E., Ratiu, Tudor S
This paper analyses continuous and discrete versions of the generalized rigid body equations and the role of these equations in numerical analysis, optimal control and integrable Hamiltonian systems....
The symmetric representation of the rigid body equations and their discretization (2002)
Bloch, Anthony M., Crouch, Peter E., Marsden, Jerrold E., Ratiu, Tudor S.
This paper analyses continuous and discrete versions of the generalized rigid body equations and the role of these equations in numerical analysis, optimal control and integrable Hamiltonian systems....
The symmetric representation of the rigid body equations and their discretization (2002)
Bloch, Anthony M., Crouch, Peter E., Marsden, Jerrold E., Ratiu, Tudor S.
This paper analyses continuous and discrete versions of the generalized rigid body equations and the role of these equations in numerical analysis, optimal control and integrable Hamiltonian systems....
Shashikanth, Banavara N., Marsden, Jerrold E., Burdick, Joel W., Kelly, Scott D.
This paper studies the dynamical fluid plus rigid-body system consisting of a two-dimensional rigid cylinder of general cross-sectional shape interacting with N point vortices. We derive the...
The Hamiltonian Structure of the Maxwell-Vlasov Equations. (2002)
Marsden,Jerrold E., Weinstein,Alan
Morrison has shown that the Maxwell-Vlasov and the Vlasov-Poisson equations for a collisionless plasma can be written in Hamiltonian form relative to a certain Poisson bracket. We derive another very...
Melkinov's Method and Arnold Diffusion for Perturbations of Integrable Hamiltonian Systems. (2002)
Holmes,Philip J., Marsden,Jerrold E.
We start with an unperturbed system containing a homoclinic orbit and at least two families of periodic orbits associated with action angle coordinates. We use KAM theory to show that some of the...
Horseshoes in Perturbations of Hamiltonian Systems with two Degress of Freedom. (2002)
Holmes,Philip J., Marsden,Jerrold E.
This paper concerns Hamiltonian and non-Hamiltonian perturbations of integrable two degree of freedom Hamiltonian systems which contain homoclinic and periodic orbits. Our main example concerns...
The equivalence of controlled lagrangian and controlled hamiltonian systems (2002)
Chang, Dong Eui, Bloch, Anthony M., Leonard, Naomi E., Marsden, Jerrold E., Woolsey, Craig A.
The symmetric representation of the rigid body equations and their discretization (2002)
Bloch, Anthony M., Crouch, Peter E., Marsden, Jerrold E., Ratiu, Tudor S.
A subspace approach to balanced truncation for model reduction of nonlinear control systems (2002)
Sanjay Lall, Jerrold E. Marsden
of nonlinear control systems
The Anisotropic Lagrangian Averaged Euler and Navier-Stokes Equations (2002)
Jerrold E. Marsden, Steve Shkoller
The purpose of this paper is twofold. First, we give a derivation of the Lagrangian averaged Euler (LAE-α) and Navier-Stokes (LANS-α) equations. This theory involves a spatial scale α and the...
Constructing a low energy transfer between Jovian moons (2002)
Wang Sang Koon, Jerrold E. Marsden, Martin W. Lo, Shane D. Ross
There has recently been considerable interest in sending a spacecraft to orbit Europa, the smallest of the four Galilean moons of Jupiter. The trajectory design involved in effecting a capture by...
VARIATIONAL PRINCIPLES FOR LIE–POISSON AND HAMILTON–POINCARÉ EQUATIONS (2002)
Hernán Cendra, Jerrold E. Marsden, Sergey Pekarsky, S. Ratiu
Dedicated to Vladimir Arnold on his 65th birthday Abstract. As is well-known, there is a variational principle for the Euler–Poincaré equations on a Lie algebra g of a Lie group G obtained by...
Clerc, Marcel G., Marsden, Jerrold E.
The 1:1 resonance for perturbed Hamiltonian systems with small dissipative and energy injection terms has been studied. These perturbations of the 1:1 resonance exhibit dissipation induced...
Controlled Lagrangians and the stabilization of mechanical systems. II. Potential shaping (2001)
Bloch, Anthony M., Chang, Dong Eui, Leonard, Naomi Ehrich, Marsden, Jerrold E.
For pt.I, see ibid., vol.45, p.2253-70 (2000). We extend the method of controlled Lagrangians (CL) to include potential shaping, which achieves complete state-space asymptotic stabilization of...
Alber, Mark S., Camassa, Roberto, Fedorov, Yuri N., Holm, Darryl D., Marsden, Jerrold E.
An extension of the algebraic-geometric method for nonlinear integrable PDE's is shown to lead to new piecewise smooth weak solutions of a class of $N$-component systems of nonlinear evolution...
Dissipation induced Instabilities and the Mechanical Laser (2001)
Clerc, Marcel G., Marsden, Jerrold E.
We study the 1:1 resonance for perturbed Hamiltonian systems with small dissipative and energy injection terms. These perturbations of the 1:1 resonance exhibit dissipation induced instabilities....
Controlled Lagrangians and the stabilization of Euler–PoincarÉ mechanical systems (2001)
Bloch, Anthony M., Leonard, Naomi Ehrich, Marsden, Jerrold E.
In this paper we develop a constructive approach to the determination of stabilizing control laws for a class of Lagrangian mechanical systems with symmetry — systems whose underlying dynamics are...
Lagrangian reduction by stages / Hernán Cendra, Jerrold E. Marsden, Tudor S. Ratiu (2001)
Marsden, Jerrold E, Ratiu, Tudor S
"July 2001, vol. 152, number 722 (third of 5 numbers)"
Abstract mechanical connection and abelian reconstruction for almost Kähler manifolds (2001)
Sergey Pekarsky, Jerrold E. Marsden
When the phase space P of a Hamiltonian G-system (P,É,G,J,H) has an almost Kähler structure a preferred connection, called abstract mechanical connection, can be defined by declaring...
J2 dynamics and formation flight (2001)
Wang Sang Koon, Jerrold E. Marsden, Richard M. Murray
We study the dynamics of the relative motion of satellites in the gravitational field of the Earth, including the effects of the bulge of the Earth (the J2 effect). Using Routh reduction and...
2001], Averaged Template Matching Equations (2001)
Anil N. Hirani, Jerrold E. Marsden, James Arvo
Abstract. By exploiting an analogy with averaging procedures in fluid dynamics, we present a set of averaged template matching equations. These equations are analogs of the exact template matching...
Geometric mechanics, Lagrangian reduction and nonholonomic systems (2001)
Hernán Cendra, Jerrold E. Marsden, Tudor S. Ratiu
This paper surveys selected recent progress in geometric mechanics, focussing on Lagrangian reduction and gives some new applications to nonholonomic systems, that is, mechanical systems with...
Kamran Mohseni, Steve Shkoller, Branko Kosović, Jerrold E. Marsden
The modeling capabilities of the Lagrangian Averaged Navier-Stokes-α equations (LANS-α) is investigated in statistically stationary three-dimensional homogeneous and isotropic turbulence. The...
Abstract mechanical connection and abelian reconstruction for almost Kahler manifolds (2001)
Sergey Pekarsky, Jerrold E. Marsden
When the phase space P of a Hamiltonian G-system (P, ω, G, J, H) has an almost Kähler structure a preferred connection, called abstract mechanical connection, canbe defined by declaring horizontal...
Abstract mechanical connection and abelian reconstruction for almost Kähler manifolds (2001)
Sergey Pekarsky, Jerrold E. Marsden
When the phase space P of a Hamiltonian G-system (P,ω,G,J,H) has an almost Kähler structure a preferred connection, called abstract mechanical connection, can be defined by declaring horizontal...
Bloch, Anthony M., Leonard, Naomi Ehrich, Marsden, Jerrold E.
We develop a method for the stabilization of mechanical systems with symmetry based on the technique of controlled Lagrangians. The procedure involves making structured modifications to the...
Conference Festschrift Arnol'd (Vladimir Igorevich) on his 60th Birthday (2000)
Bierstone, Edward, Khesin, Boris A, Khovanskii, Askold, Marsden, Jerrold E
Abstract mechanical connection and Abelian reconstruction for almost Kahler manifolds (2000)
Pekarsky, Sergey, Blaom, Anthony D., Marsden, Jerrold E.
When the phase space P of a Hamiltonian G-system (P, \omega, G, J, H) has an almost Kahler structure a preferred connection, called abstract mechanical connection, can be defined by declaring...
Stabilization of relative equilibria (2000)
Jalnapurkar, Sameer M., Marsden, Jerrold E.
This paper discusses the problem of obtaining feedback laws to asymptotically stabilize relative equilibria of mechanical systems with symmetry. We show how to stabilize an internally unstable...
Reduction theory and the Lagrange–Routh equations (2000)
Marsden, Jerrold E., Ratiu, Tudor S., Scheurle, Jürgen
Reduction theory for mechanical systems with symmetry has its roots in the classical works in mechanics of Euler, Jacobi, Lagrange, Hamilton, Routh, Poincare, and others. The modern vision of...
Koon, Wang Sang, Lo, Martin W., Marsden, Jerrold E., Ross, Shane D.
In this paper we apply dynamical systems techniques to the problem of heteroclinic connections and resonance transitions in the planar circular restricted three-body problem. These related phenomena...
Reduction theory and the Lagrange–Routh equations (2000)
Marsden, Jerrold E., Ratiu, Tudor S., Scheurle, Jürgen
Reduction theory for mechanical systems with symmetry has its roots in the classical works in mechanics of Euler, Jacobi, Lagrange, Hamilton, Routh, Poincaré, and others. The modern vision of...
The anisotropic averaged Euler equations (2000)
Marsden, Jerrold E., Shkoller, Steve
The purpose of this paper is to derive the anisotropic averaged Euler equations and to study their geometric and analytic properties. These new equations involve the evolution of a mean velocity...
Variational methods, multisymplectic geometry and continuum mechanics (2000)
Marsden, Jerrold E., Pekarsky, Sergey, Shkoller, Steve, West, Matthew
This paper presents a variational and multisymplectic formulation of both compressible and incompressible models of continuum mechanics on general Riemannian manifolds. A general formalism is...
Symmetry reduction of discrete Lagrangian mechanics on Lie groups (2000)
Marsden, Jerrold E., Pekarsky, Sergey, Shkoller, Steve
For a discrete mechanical system on a Lie group $G$ determined by a (reduced) Lagrangian $\ell$ we define a Poisson structure via the pull-back of the Lie-Poisson structure on the dual of the Lie...
Dynamical systems, the three-body problem and space mission design (2000)
Wang Sang Koon, Martin W. Lo, Jerrold E. Marsden, Shane D. Ross
This paper concerns heteroclinic connections and resonance transitions in the planar circular restricted 3-body problem, with applications to the dynamics of comets and asteroids and the design of...
Anthony M. Bloch, Dong Eui Chang, Naomi Ehrich Leonard, Jerrold E. Marsden
Abstract—Weextend the method of controlled Lagrangians (CL) to include potential shaping, which achieves complete state-space asymptotic stabilization of mechanical systems. The CL method deals...
Reduction theory and the Lagrange-Routh Equations (2000)
Jerrold E. Marsden, Tudor S. Ratiu, Jürgen Scheurle
Reduction theory for mechanical systems with symmetry has its roots in the classical works in mechanics of Euler, Jacobi, Lagrange, Hamilton, Routh, Poincaré and others. The modern vision of...
1999b] Symmetry Reduction of Discrete Lagrangian Mechanics on Lie groups preprint (2000)
Jerrold E. Marsden, Sergey Pekarsky, Steve Shkoller
Abstract. For a discrete mechanical system on a Lie group G determined by a (reduced) Lagrangian ℓ we define a Poisson structure via the pull-back of the Lie-Poisson structure on the dual of the...
2000a] Potential and kinetic shaping for control of underactuated mechanical systems (2000)
Anthony M. Bloch, Naomi Ehrich Leonard, Woolsey As, Dong Eui Chang, Jerrold E. Marsden
Proc. Amer. Control Conf., (2000), 3913–3917. This paper combines techniques of potential shaping with those of kinetic shaping to produce some new methods for stabilization of mechanical control...
Halo Orbit Mission Correction Maneuvers Using Optimal Control (2000)
Radu Serban, Wang S. Koon, Martin W. Lo, Jerrold E. Marsden, Linda R. Petzold, Shane D. Ross, ...
This paper addresses the computation of the required trajectory correction maneuvers #TCM# for a halo orbit space mission to compensate for the launch velocity errors introduced by inaccuracies of...
Structure-Preserving Model Reduction of Mechanical Systems. (2000)
Sanjay Lall Petr, Petr Krysl, Jerrold E. Marsden
We provide an explicit method of constructing reduced-order models of mechanical systems which preserves the Lagrangian structure of the original system. These methods may be used in combination with...
A Subspace Approach to Balanced Truncation for Model Reduction of Nonlinear Control Systems (2000)
Sanjay Lall, Jerrold E. Marsden, Sonja Glavaski
In this paper we introduce a new method of model reduction for nonlinear control systems. Our approach is to construct an approximately balanced realization. The method requires only standard matrix...
Discrete Euler-Poincaré and Lie-Poisson equations (1999)
Marsden, Jerrold E., Pekarsky, Sergey, Shkoller, Steve
In this paper, discrete analogues of Euler–Poincare and Lie–Poisson reduction theory are developed for systems on finite dimensional Lie groups G with Lagrangians L : TG → R that are...
Discrete Euler-Poincar\'{e} and Lie-Poisson Equations (1999)
Marsden, Jerrold E., Pekarsky, Sergey, Shkoller, Steve
In this paper, discrete analogues of Euler-Poincar\'{e} and Lie-Poisson reduction theory are developed for systems on finite dimensional Lie groups $G$ with Lagrangians $L:TG \to {\mathbb R}$ that...
Model reduction for analysis of cascading failures in power systems (1999)
Parrilo, Pablo A., Lall, Sanjay, Paganini, Fernando, Verghese, George C., Lesieutre, Bernard C., Marsden, Jerrold E.
In this paper, we apply a principal-orthogonal decomposition based method to the model reduction of a hybrid, nonlinear model of a power network. The results demonstrate that the sequence of fault...
The Euler-Poincare Equations in Geophysical Fluid Dynamics (1999)
Holm, Darryl D., Marsden, Jerrold E., Ratiu, Tudor S.
Recent theoretical work has developed the Hamilton's-principle analog of Lie-Poisson Hamiltonian systems defined on semidirect products. The main theoretical results are twofold: (1) Euler-Poincar\'e...
A Nonlinear Analysis of the Averaged Euler Equations (1999)
Holm, Darryl D., Kouranbaeva, Shinar, Marsden, Jerrold E., Ratiu, Tudor, Shkoller, Steve
This paper develops the geometry and analysis of the averaged Euler equations for ideal incompressible flow in domains in Euclidean space and on Riemannian manifolds, possibly with boundary. The...
Stabilization of the pendulum on a rotor arm by the method of controlled Lagrangians (1999)
Bloch, Anthony M., Leonard, Naomi Ehrich, Marsden, Jerrold E.
Obtains feedback stabilization of an inverted pendulum on a rotor arm by the “method of controlled Lagrangians”. This approach involves modifying the Lagrangian for the uncontrolled system so...
Introduction to Mechanics and Symmetry : A Basic Exposition of Classical Mechanical Systems (1999)
Marsden, Jerrold E., Ratiu, Tudor S.
Contenido: Sistemas hamiltonianos en espacios lineales simplécticos; Variedades, campos vectoriales y formas diferenciales; Sistemas hamiltonianos en variedades simplécticas; Mecánica lagrangiana;...
Introduction to Mechanics and Symmetry : A Basic Exposition of Classical Mechanical Systems (1999)
Marsden, Jerrold E., Ratiu, Tudor S.
0-387-98643-X
The Lyapunov-Malkin Theorem and Stabilization of the Unicycle with Rider, preprint (1999)
Dmitry V. Zenkov, Anthony M. Bloch, Jerrold E. Marsden
This paper analyzes stabilization of a nonholonomic system consisting of a unicycle with rider. It is shown that one can achieve stability of slow steady vertical motions by imposing a feedback...
2000], The Orbit Bundle Picture of Cotangent Bundle Reduction (1999)
Jerrold E. Marsden, Matthew Perlmutter
Cotangent bundle reduction theory is a basic and well developed subject in which one performs symplectic reduction on cotangent bundles. One starts with a (free and proper) action of a Lie group G on...
Discrete Euler-Poincaré and Lie-Poisson equations (1999)
Jerrold E. Marsden, Sergey Pekarsky, Steve Shkoller
Abstract. In this paper, discrete analogues of Euler-Poincaré and Lie-Poisson reduction theory are developed for systems on finite dimensional Lie groups G with Lagrangians L: TG → R that are...
1997] Multisymplectic geometry, covariant Hamiltonians and water waves (1999)
Jerrold E. Marsden, Steve Shkoller
This paper concerns the development and application of the multisymplectic Lagrangian and Hamiltonian formalism for nonlinear partial differential equations. This theory generalizes and unifies the...
2000], The Orbit Bundle Picture of Cotangent Bundle Reduction (1999)
Jerrold E. Marsden, Matthew Perlmutter
Cotangent bundle reduction theory is a basic and well developed subject in which one performs symplectic reduction on cotangent bundles. One starts with a (free and proper) action of a Lie group G on...
Empirical Model Reduction of Controlled Nonlinear Systems (1999)
Sanjay Lall, Jerrold E. Marsden, Sonja Glavaski
In this paper we introduce a new method of model reduction for nonlinear systems with inputs and outputs. The method requires only standard matrix computations, and when applied to linear systems...
Empirical Model Reduction of Controlled Nonlinear Systems (1999)
Sanjay Lall, Jerrold E. Marsden, Sonja Glavaski
In this paper we introduce a new method of model reduction for nonlinear systems with inputs and outputs. The method requires only standard matrix computations, and when applied to linear systems...
The Lyapunov-Malkin Theorem and Stabilization (1999)
Of The Unicycle, Dmitry V. Zenkov, Anthony M. Bloch, Jerrold E. Marsden
This paper analyzes stabilization of a nonholonomic system consisting of a unicycle with rider. It is shown that one can achieve stability of slow steady vertical motions by imposing a feedback...
On billiard solutions of nonlinear PDEs (1999)
Mark S. Alber, Roberto Camassa, Yuri N. Fedorov, Darryl D. Holm, Jerrold E. Marsden
This letter presents some special features of a class of integrable PDE’s admitting billiard-type solutions, which set them apart from equations whose solutions are smooth, such as the KdV...
Discrete rigid body dynamics and optimal control (1998)
Bloch, Anthony M., Crouch, Peter E., Marsden, Jerrold E., Ratiu, Tudor S.
We analyze an alternative formulation of the rigid body equations, their relationship with the discrete rigid body equations of Moser-Veselov (1991) and their formulation as an optimal control...
Model reduction, centering, and the Karhunen-Loeve expansion (1998)
Glavaški, Sonja, Marsden, Jerrold E., Murray, Richard M.
We propose a new computationally efficient modeling method that captures a given translation symmetry in a system. To obtain a low order approximate system of ODEs, prior to performing a Karhunen...
Point vortices on a sphere: Stability of relative equilibria (1998)
Pekarsky, Sergey, Marsden, Jerrold E.
In this paper we analyze the dynamics of N point vortices moving on a sphere from the point of view of geometric mechanics. The formalism is developed for the general case of N vortices, and the...
Posbergh, Thomas A., Krishnaprasad, P. S., Marsden, Jerrold E.
The authors consider a system consisting of a rigid body to which a linear extensible shear beam is attached. For such a system the Energy-Casimir method can be used to investigate the stability of...
Simo, Juan C., Marsden, Jerrold E., Krishnaprasad, P. S.
It is our belief that a thorough understanding of the mathematical underpinnings of elasticity is crucial to its analytical and numerical implementation. For example, in the analysis of rotating...
The Dynamics of Two Coupled Rigid Bodies, (1998)
Grossman, R., Krishnaprasad, P. S., Marsden, Jerrold E.
In this paper we derive a Poisson bracket on the phase space so(3) x so(3) x SO(3) such that the dynamics of two three dimensional rigid bodies coupled by a ball and socket joint can be written as a...
Nonlinear Stability in Fluid and Plasma Dynamics. (1998)
This report presents a block diagonalization theorem which is designed to study the stability and bifurcation of rotating systems, or more generally, of relative equilibria. The context of the...
Dynamics of Deformable Bodies. (1998)
The main achievement in this grant were developing a scientific understanding of the role of variational principles in symplectic and energy - momentum integrators, and using this structure to study...
The workshop reinforced the idea that a combination of analysis, simulation, and experiment continues to be a feasible approach to the problem of combustion instabilities. Control of these...
Robust Nonlinear Control Theory with Applications to Aerospace Vehicles (1998)
Murray, Richard M., Balas, Gary, Doyle, John C., Marsden, Jerrold E.
The focus of this program is fundamental research in general methods of analysis and design of complex uncertain nonlinear systems. The approach builds on our recent success in blending robust and...
Formation Flight of Micro-Satellite Clusters (1998)
Murray, Richard M., Marsden, Jerrold E.
One of the significant challenges to successful formation flight of spacecraft is maintenance of the formation, i.e., control of the motion of the individual spacecraft to maintain the overall...
Compressible Flow Modeling with the Lagrangian Averaged Navier-Stokes Equations (1998)
Marsden, Jerrold E., Mohseni, Kamran, Dimotakix, Paul E.
We have derived, in a mathematically precise way, Lagrangian-averaged models for incompressible and compressible flow. This work has now appeared in the SIAM Journal "Multiscale Modeling and...
Multisymplectic geometry, covariant Hamiltonians, and water waves (1998)
Marsden, Jerrold E., Shkoller, Steve
This paper concerns the development and application of the multisymplectic Lagrangian and Hamiltonian formalism for nonlinear partial differential equations. In this theory, solutions of a PDE are...
Multisymplectic geometry, variational integrators, and nonlinear PDEs (1998)
Marsden, Jerrold E., Patrick, George W., Shkoller, Steve
This paper presents a geometric-variational approach to continuous and discrete mechanics and field theories. Using multisymplectic geometry, we show that the existence of the fundamental geometric...
The Maxwell–Vlasov equations in Euler–Poincaré form (1998)
Cendra, Hernán, Holm, Darryl D., Hoyle, Mark J. W., Marsden, Jerrold E.
Low's well-known action principle for the Maxwell–Vlasov equations of ideal plasma dynamics was originally expressed in terms of a mixture of Eulerian and Lagrangian variables. By imposing suitable...
Euler-Poincaré Models of Ideal Fluids with Nonlinear Dispersion (1998)
Holm, Darryl D., Marsden, Jerrold E., Ratiu, Tudor S.
We propose a new class of models for the mean motion of ideal incompressible fluids in three dimensions, including stratification and rotation. In these models, the amplitude of the rapid...
Momentum Maps and Classical Relativistic Fields. Part I: Covariant Field Theory (1998)
Gotay, Mark J., Isenberg, James, Marsden, Jerrold E., Montgomery, Richard
This is the first paper of a five part work in which we study the Lagrangian and Hamiltonian structure of classical field theories with constraints. Our goal is to explore some of the connections...
Matching and stabilization by the method of controlled Lagrangians (1998)
Bloch, Anthony M., Leonard, Naomi Ehrich, Marsden, Jerrold E.
We describe a class of mechanical systems for which the “method of controlled Lagrangians” provides a family of control laws that stabilize an unstable (relative) equilibrium. The controlled...
Análisis clásico elemental (1998)
Marsden, Jerrold E., Hoffman, Michael J.
Traducción de: Elementary classsical analysis
Marsden, Jerrold E., Hoffman, Michael J.
Traducción de: Elementary classsical analysis
Análisis clásico elemental / Jerrold E. Marsden, Michael J,. Hoffman (1998)
Marsden, Jerrold E, Hoffman, Michael J
Traducción de: Elementary classical analysis
Cálculo vectorial / Jerrold E. Marsden, Anthony J. Tromba (1998)
Marsden, Jerrold E, Tromba, Anthony J
Traducción de: Vector calculus
Lagrangian reduction, the Euler-Poincaré equations, and semidirect products (1998)
Cendra, Hernán, Holm, Darryl D., Marsden, Jerrold E., Ratiu, Tudor S.
Symplectic reduction for semidirect products and central extensions (1998)
Marsden, Jerrold E., Misiolek, Gerard, Perlmutter, Matthew, Ratiu, Tudor S.
Euler-Poincaré models of ideal fluids with nonlinear dispersion, Phys (1998)
Darryl D. Holm, Jerrold E. Marsden, Tudor S. Ratiu
nonlinear dispersion
Model reduction, centering, and the Karhunen-lo`eve expansion (1998)
Jerrold E. Marsden, Richard M. Murray
We propose a new computationally efficient modeling method that captures existing translation symmetry in a system. To obtain a low order approximate system of ODEs prior to performing Karhunen Loeve...
The Maxwell-Vlasov equations in Euler-Poincaré form (1998)
Hernán Cendra, Darryl D. Holm, Jerrold E. Marsden
Low’s well known action principle for the Maxwell-Vlasov equations of ideal plasma dynamics was originally expressed in terms of a mixture of Eulerian and Lagrangian variables. By imposing suitable...
Symmetries in motion: Geometric foundations of motion control (1998)
Jerrold E. Marsden, Jim Ostrowski
Some interesting aspects of motion and control for systems such as those found in biological and robotic locomotion, attitude control of spacecraft and underwater vehicles, and steering of cars and...
Euler-poincaré equations and semidirect products with applications to continuum theories (1998)
Darryl D. Holm, Jerrold E. Marsden, Tudor S. Ratiu
We study Euler–Poincaré systems (i.e., the Lagrangian analogue of Lie-Poisson Hamiltonian systems) defined on semidirect product Lie algebras. We first give a derivation of the Euler–Poincaré...
Geometric phases, reduction and Lie-Poisson structure for the resonant three-wave interaction (1998)
Mark S. Alber, Gregory G. Luther, Jerrold E. Marsden, Jonathan M. Robbins
Hamiltonian Lie-Poisson structures of the three-wave equations associated with the Lie algebras su(3) and su(2, 1) are derived and shown to be compatible. Poisson reduction is performed using the...
Discrete rigid body dynamics and optimal control (1998)
Anthony M. Bloch, Jerrold E. Marsden
In this paper we analyze an alternative formulation of the rigid body equations, their relationship with the discrete rigid body equations of Moser–Veselov and their formulation as an optimal...
Symplectic reduction for semidirect products and central extensions, Diff (1998)
Jerrold E. Marsden, Tudor S. Ratiu, Matthew Perlmutter
This paper proves a symplectic reduction by stages theorem in the context of geometric mechanics on symplectic manifolds with symmetry groups that are group extensions. We relate the work to the...
Stability of Relative Equilibria of Point Vortices on a Sphere and (1998)
Symplectic Integrators, Jerrold E. Marsden, Sergey Pekarsky, Steve Shkoller
Summary. — This paper analyzes the dynamics of N point vortices moving on a sphere from the point of view of geometric mechanics. The formalism is developed for the general case of N vortices, and...
Multisymplectic geometry, variational integrators, and nonlinear PDEs (1998)
Jerrold E. Marsden, George W. Patrick, Steve Shkoller
Abstract: This paper presents a geometric-variational approach to continuous and discrete mechanics and field theories. Using multisymplectic geometry, we show that the existence of the fundamental...
The poisson reduction of nonholonomic mechanical systems (1998)
Wang Sang Koon, Jerrold E. Marsden
This paper continues the work of Koon and Marsden [1997b] that began the comparison of the Hamiltonian and Lagrangian formulations of nonholonomic systems. Because of the necessary replacement of...
Symplectic reduction for semidirect products and central extensions, Diff (1998)
Jerrold E. Marsden, Tudor S. Ratiu, Matthew Perlmutter
This paper proves a symplectic reduction by stages theorem in the context of geometric mechanics on symplectic manifolds with symmetry groups that are group extensions. We relate the work to the...
Symplectic reduction for semidirect products and central extensions, Diff (1998)
Jerrold E. Marsden, Gerard Misiolek, Matthew Perlmutter, Tudor S. Ratiu
to appear in Di#erential Geometry and its Applications MS2000 Classification 37J15, 53D20 This paper proves a symplectic reduction by stages theorem in the context of geometric mechanics on...
The Euler-Poincaré Equations and Semidirect Products with Applications to Continuum Theories (1998)
Darryl D. Holm, Jerrold E. Marsden, Tudor S. Ratiu
We study Euler--Poincare systems (i.e., the Lagrangian analogue of LiePoisson Hamiltonian systems) defined on semidirect product Lie algebras. We first give a derivation of the Euler--Poincare...
Euler-Poincaré models of ideal fluids with nonlinear dispersion (1998)
Darryl D. Holm, Jerrold E. Marsden, Tudor S. Ratiu
Based on recent advances in the theory of Euler--Poincare (EP) equations with advected parameters and using the methods of Hamilton's principle asymptotics and averaged Lagrangians, we propose a...
Stabilization of Relative Equilibria II (1998)
Sameer M. Jalnapurkar, Jerrold E. Marsden
In this paper, we obtain feedback laws to asymptotically stabilize relative equilibria of mechanical systems with symmetry. We use a notion of stability `modulo the group action' developed by...
Stabilization of Relative Equilibria (1998)
Sameer M. Jalnapurkar, Jerrold E. Marsden
This paper discusses the problem of obtaining feedback laws to asymptotically stabilize relative equilibria of mechanical systems with symmetry. We show how to stabilize an internally unstable...
Symmetries in Motion: Geometric Foundations of Motion Control (1998)
Jerrold E. Marsden, Jim Ostrowski
Some interesting aspects of motion and control for systems such as those found in biological and robotic locomotion, attitude control of spacecraft and underwater vehicles, and steering of cars and...
Multisymplectic geometry, variational integrators, and nonlinear PDEs (1998)
Jerrold E. Marsden, George W. Patrick, Steve Shkoller
Abstract: This paper presents a geometric-variational approach to continuous and discrete mechanics and field theories. Using multisymplectic geometry, we show that the existence of the fundamental...
Symplectic Reduction for Semidirect Products and Central Extensions (1998)
Jerrold E. Marsden, Gerard Misiołek, Matthew Perlmutter, Tudor S. Ratiu
This paper proves a symplectic reduction by stages theorem in the context of geometric mechanics on symplectic manifolds with symmetry groups that are group extensions. We relate the work to the...
Geometric Phases, Reduction and Lie-Poisson Structure for the Resonant Three-wave Interaction (1998)
Mark S. Alber, Gregory G. Luther, Jerrold E. Marsden, Jonathan M. Robbins
Hamiltonian Lie-Poisson structures of the three-wave equations associated with the Lie algebras su(3) and su(2, 1) are derived and shown to be compatible.
The symmetric representation of the rigid body equations and their discretization (1998)
Anthony M. Bloch, Peter E. Crouch, Jerrold E. Marsden, Tudor S. Ratiu
This paper analyzes continuous and discrete versions of the generalized rigid body equations and the role of these equations in numerical analysis, optimal control and integrable Hamiltonian systems....
The geometric structure of nonholonomic mechanics (1997)
Koon, Wang Sang, Marsden, Jerrold E.
Many important problems in multibody dynamics, the dynamics of wheeled vehicles and motion generation, involve nonholonomic mechanics. Many of these systems have symmetry, such as the group of...
Stabilization of mechanical systems using controlled Lagrangians (1997)
Bloch, Anthony M., Leonard, Naomi Ehrich, Marsden, Jerrold E.
We propose an algorithmic approach to stabilization of Lagrangian systems. The first step involves making admissible modifications to the Lagrangian for the uncontrolled system, thereby constructing...
The Energy-Momentum Method for the Stability of Nonholonomic Systems (1997)
Zenkov, Dmitry V., Bloch, Anthony M., Marsden, Jerrold E.
In this paper we analyze the stability of relative equilibria of nonholonomic systems (that is, mechanical systems with nonintegrable constraints such as rolling constraints). In the absence of...
Energy dependent Schrödinger operators and complex Hamiltonian systems on Riemann surfaces (1997)
Alber, Mark S., Luther, Gregory G., Marsden, Jerrold E.
We use so-called energy-dependent Schrödinger operators to establish a link between special classes of solutions on N-component systems of evolution equations and finite dimensional Hamiltonian...
The Hamiltonian and Lagrangian approaches to the dynamics of nonholonomic systems (1997)
Wang Sang Koon, Jerrold E. Marsden
This paper compares the Hamiltonian approach to systems with nonholonomic constraints (see Weber [1982], Arnold [1988], and Bates and Sniatycki [1993], van der Schaft and Maschke [1994] and...
Geometry and control of three-wave interactions (1997)
Mark S. Alber, Gregory G. Luther, Jerrold E. Marsden, Jonathan M. Robbins
The integrable structure of the three-wave equations is discussed in the setting of geometric mechanics. Lie-Poisson structures with quadratic Hamiltonian are associated with the three-wave equations...
Naomi Ehrich Leonard, Jerrold E. Marsden
This paper develops the stability theory of relative equilibria for mechanical systems with symmetry. It is especially concerned with systems that have a noncompact symmetry group, such as the group...
Wang-sang Koon, Jerrold E. Marsden
In this paper we establish necessary conditions for optimal control using the ideas of Lagrangian reduction in the sense of reduction under a symmetry group. The techniques developed here are...
The Geometric Structure of Nonholonomic Mechanics (1997)
Wang Sang Koon, Jerrold E. Marsden
Many important problems in multibody dynamics, the dynamics of wheeled vehicles and motion generation, involve nonholonomic mechanics. Many of these systems have symmetry, such as the group of...
Wang-Sang Koon, Jerrold E. Marsden, E. Marsden
. In this paper we establish necessary conditions for optimal control using the ideas of Lagrangian reduction in the sense of reduction under a symmetry group. The techniques developed here are...
Mechanical Integrators Derived from a Discrete Variational Principle (1997)
Jeffrey Wendlandt, Jerrold E. Marsden
Many numerical integrators for mechanical system simulation are created by using discrete algorithms to approximate the continuous equations of motion. In this paper, we present a procedure to...
Lagrangian Reduction, the Euler-Poincaré Equations, and Semidirect Products (1997)
Hernan Cendra, Darryl D. Holm, Jerrold E. Marsden, Tudor S. Ratiu
There is a well developed and useful theory of Hamiltonian reduction for semidirect products, which applies to examples such as the heavy top, compressible fluids and MHD, which are governed by...
The Hamiltonian and Lagrangian Approaches to the Dynamics of Nonholonomic Systems (1997)
Wang Sang Koon, Jerrold E. Marsden
This paper compares the Hamiltonian approach to systems with nonholonomic constraints (see Weber [1982], Arnold [1988], and Bates and Sniatycki [1993], van der Schaft and Maschke [1994] and...
zenkovQmat h.ohio-state.edu ablochQmath.lsa.umich.edu Contents (1997)
Dmitry V. Zenkov, Anthony M. Bloch, Jerrold E. Marsden, Jerrold E. Marsdenz
The Hamiltonian and Lagrangian approaches to the dynamics of nonholonomic systems (1997)
Wang-sang Koon, Wang-sang Koon, Jerrold E. Marsden, Jerrold E. Marsden
This paper compares the Hamiltonian approach to systems with nonholonomic constraints (see Weber [1982], Arnold [1988], and Bates and Snyatycki [1992], Van der Schaft and Maschke [I9941 and...
Nonholonomic Mechanical Systems with Symmetry (1996)
Krishnaprasad, P.S., Bloch, Anthony M., Marsden, Jerrold E., Murray, Richard M.
This work develops the geometry and dynamics of mechanical systems with nonholonomic constraints and symmetry from the perspective of Lagrangian mechanics and with a view to control-theoretical...
Nonholonomic mechanical systems with symmetry (1996)
Bloch, Anthony M., Murray, Richard M., Marsden, Jerrold E., Krishnaprasad, P. S.
This work develops the geometry and dynamics of mechanical systems with nonholonomic constraints and symmetry from the perspective of Lagrangian mechanics and with a view to control-theoretical...
The Hamiltonian and Lagrangian approaches to the dynamics of nonholonomic systems (1996)
Marsden, Jerrold E., Koon, Wang-Sang
This paper compares the Hamiltonian approach to systems with nonholonomic constraints (see Weber [1982], Arnold [1988], and Bates and Snyatycki [1992], Van der Schaft and Maschke [I9941 and...
Mechanical integrators derived from a discrete variational principle (1996)
Wendland, Jeffrey M., Marsden, Jerrold E
Many numerical integrators for mechanical system simulation are created by using discrete algorithms to approximate the continuous equations of motion. In this paper, we present a procedure to...
The Euler-Poincaré equations and double bracket dissipation (1996)
Ratiu, Tudor S., Krishnaprasad, P. S., Bloch, Anthony M., Marsden, Jerrold E.
This paper studies the perturbation of a Lie-Poisson (or, equivalently an Euler-Poincaré) system by a special dissipation term that has Brockett's double bracket form. We show that a formally...
The Euler-Poincaré equations and double bracket dissipation (1996)
Bloch, Anthony, Krishnaprasad, P. S., Marsden, Jerrold E., Ratiu, Tudor S.
Análisis básico de variable compleja (1996)
Marsden, Jerrold E., Hoffman, Michael J.
Traducción de: Basic Complex Analysis
Marsden, Jerrold E., Hoffman, Michael J.
Traducción de: Basic Complex Analysis
The Euler-Poincaré equations and double bracket dissipation (1996)
Bloch, Anthony M., Krishnaprasad, P. S., Marsden, Jerrold E., Ratiu, Tudor S.
Chong-ye Xu, Jerrold E. Marsden
This paper establishes abstract results, which extend those of Potier–Ferry and Sobolevskii, on global existence and stability of solutions to quasilinear equations near an equilibrium point whose...
Wang-sang Koon, Jerrold E. Marsden
In this paper we establish necessary conditions for optimal control using the ideas of Lagrangian reduction in the sense of reduction under a symmetry group. The techniques developed here are...
The Euler-Poincar'e Equations and Double Bracket Dissipation (1996)
Anthony Bloch, P. S. Krishnaprasad, Jerrold E. Marsden, Tudor S. Ratiu
This paper studies the perturbation of a Lie-Poisson (or, equivalently an Euler-Poincaré) system by a special dissipation term that has Brockett’s double bracket form. We show that a formally...
Nonholonomic mechanical systems with symmetry (1996)
Anthony M. Bloch, P. S. Krishnaprasad, Jerrold E. Marsden, Richard M. Murray, Communicated P. Holmes
Vivien Kirk, Jerrold E. Marsden, Mary Silber
This paper uses Hamiltonian methods to find and determine the stability of some new solution branches for an equivariant Hopf bifurcation on C 4. The normal form has a symmetry group given by the...
Nonholonomic Mechanical Systems with Symmetry (1996)
Anthony M. Bloch, P.S. Krishnaprasad, Jerrold E. Marsden, Richard M. Murray
This work develops the geometry and dynamics of mechanicalsystems with nonholonomic constraints and symmetry from the perspective of Lagrangian mechanics and with a view to control theoretical...
Nonholonomic mechanical systems with symmetry (1996)
Anthony M. Bloch, P. S. Krishnaprasad, Jerrold E. Marsden, Richard M. Murray, Communicated R Holmes
Abstract......................................... 21
Joint-space tracking of workspace trajectories in continuous time (1995)
Getz, Neil H., Marsden, Jerrold E.
We present a controller for a class of robotics manipulators which provides exponential convergence to a desired end-effector trajectory using gains specified in joint-space. This is accomplished...
A dynamic inverse for nonlinear maps (1995)
Getz, Neil H., Marsden, Jerrold E.
We consider the problem of estimating the time-varying root of a time-dependent nonlinear map. We introduce a "dynamic inverse" of a map, another generally time-dependent map which one composes with...
Dynamic inversion and polar decomposition of matrices (1995)
Getz, Neil H., Marsden, Jerrold E.
Using the recently introduced concept of a "dynamic inverse" of a map, along with its associated analog computational paradigm. we construct continuous-time nonlinear dynamical systems which produce...
Koon, Wang-Sang, Marsden, Jerrold E.
In this paper we establish necessary conditions for optimal control using the ideas of Lagrangian reduction in the sense of reduction under a symmetry group. The techniques developed here are...
Pattern Evocation and Geometric Phases in Mechanical Systems with Symmetry (1995)
Marsden, Jerrold E., Scheurle, Jürgen
This paper is concerned with the relation between the dynamics of a given Hamiltonian system with a given symmetry group and its reduced dynamics. We illustrate the process of visualization of...
Control for an Autonomous Bicycle (1995)
Neil H. Getz, Jerrold E. Marsden
The control of nonholonomic and underactuated systems with symmetry is illustrated by the problem of controlling a bicycle. We derive a controller which, using steering and rear-wheel torque, causes...
Tracking Implicit Trajectories (1995)
Neil Getz, Neil H. Getz, Jerrold E. Marsden, Jerrold E. Marsden
Output tracking of implcitly defined reference trajectories is examined. A continuous-time nonlinear dynamical system is constructed that produces explicit estimates of time-varying implicit...
Jerrold E. Marsden, Dynamical Systems, Je�rey M. Wendlandt
This paper explores pattern evocation and the visualization of orbits of the double spherical pendulum. Pattern evocation is a phenomenon where patterns emerge when the �ow of a dy� namical...
Control for an autonomous bicycle (1995)
Neil H. Getz, Jerrold E. Marsden
The control of nonholonomic and underactuated systems with symmetry is illustrated by the problem of controlling a bicycle. We derive a controller which, using steering and rear-wheel torque, causes...
Dissipation induced instabilities (1994)
Bloch, Anthony M., Krishnaprasad, P. S., Marsden, Jerrold E., Ratiu, Tudor S.
Normal forms for threedimensional parametric instabilities (1994)
Edgar Knobloch, Alex Mahalov, Jerrold E. Marsden
We derive and analyze several low dimensional Hamiltonian normal forms describing system symmetry breaking in ideal hydrodynamics. The equations depend on two parameters (ɛ, λ), where ɛ is the...
Dissipation induced instabilities (1994)
Anthony Bloch, P. S. Krishnaprasad, Jerrold E. Marsden, Tudor S. Ratiu
The main goal of this paper is to prove that if the energy-momentum (or energy-Casimir) methodpredicts formal instability of a relative equilibrium in a Hamiltonian system with symmetry, then with...
The Euler-Poincaré Equations and Double Bracket Dissipation (1994)
Anthony Bloch, P. S. Krishnaprasad, Jerrold E. Marsden, Tudor S. Ratiu
This paper studies the perturbation of a Lie-Poisson (or, equivalently an Euler-Poincaré) system by a special dissipation term that has Brockett's double bracket form. We show that a formally...
Dissipation Induced Instabilities (1993)
Bloch, Anthony, Krishnaprasad, P. S., Marsden, Jerrold E., Ratiu, Tudor S.
The main goal of this paper is to prove that if the energy-momentum (or energy-Casimir) method predicts formal instability of a relative equilibrium in a Hamiltonian system with symmetry, then with...
Cálculo vectorial : problemas resueltos / Jerrold E. Marsden y Anthony J. Tromba (1993)
Marsden, Jerrold E, Tromba, Anthony J
Traducción de: Study guide for vector calculus
The reduced euler-lagrange equations (1993)
Jerrold E. Marsden, Jürgen Scheurle
Marsden and Scheurle [1993] studied Lagrangian reduction in the context of momentum map constraints—here meaning the reduction of the standard Euler-Lagrange system restricted to a level set of a...
Lagrangian reduction and the double spherical pendulum (1993)
Jerrold E. Marsden, Jürgen Scheurle
This paper studies the stability and bifurcations of the relative equilibria of the double spherical pendulum, which has the circle as its symmetry group. This example as well as others with...
The Erwin, Schrödinger International Boltzmanngasse, Anthony Bloch, Jerrold E. Marsden, Tudor S. Ratiu, Anthony Bloch, ...
This paper studies the perturbation of a Lie-Poisson (or, equivalently an Euler-Poincaré) system by a special dissipation term that has Brockett’s double bracket form. We show that a formally...
Generic bifurcation of Hamiltonian vector fields with symmetry (1992)
Dellnitz, Michael, Melbourne, Ian, Marsden, Jerrold E.
One of the goals of this paper is to describe explicitly the generic movement of eigenvalues through a one-to-one resonance in a linear Hamiltonian system which is equivariant with respect to a...
A Mathematical introduction to fluid mechanics (1992)
Chorin, Alexander Joel, Marsden, Jerrold E.
Incluye índice
A Mathematical introduction to fluid mechanics / A.J. Chorin, Jerrold E. Marsden. (1992)
Chorin, Alexander Joel, Marsden, Jerrold E.
Incluye índice
Marsden, Jerrold E, Moncrief, Vincent
Incluye bibliografía
Dissipation Induced Instabilities (1992)
Bloch, Anthony M., Krishnaprasad, P.S., Marsden, Jerrold E., Ratiu, Tudor S.
The main goal of this paper is to prove that if the energy- momentum (or energy-Casimir) method predicts formal instability of a relative equilibrium in a Hamiltonian system with symmetry, then with...
Dissipation Induced Instabilities (1992)
Bloch, Anthony M., Krishnaprasad, P.S., Marsden, Jerrold E., Ratiu, Tudor S.
The main goal of this paper is to prove that if the energy- momentum (or energy-Casimir) method predicts formal instability of a relative equilibrium in a Hamiltonian system with symmetry, then with...
The heavy top: a geometric treatment (1992)
Lewis, Debra, Ratiu, Tudor S., Simo, J. C., Marsden, Jerrold E.
1992] Generic bifurcation of Hamiltonian vector fields with symmetry, Nonlinearity 5 (1992)
Michael Dellnitz, Ian Melbourne, Jerrold E. Marsden
One of the goals of this paper is to describe explicitly the generic movement of eigenvalues through a one-to-one resonance in a (linearized) Hamiltonian sys-tem. We classify this movement, and hence...
This paper gives an overview of selected topics in mechanics and their relation to questions of stability, control and stabilization. The mechanical connection, whose holonomy gives phases and that...
1992] Stress-energy-momentum tensors and the Belifante-Resenfeld formula (1992)
We present a new method of constructing a stress-energy-momentum tensor for a classical field theory based on covariance considerations and Noether theory. The stress-energy-momentum tensor T µ ν...
Duration and Change: Fifty years at Oberwolfach, (1992)
Jerrold E. Marsden, M. Artin, H. Kraft, R. Remmert
This paper gives a few new developments in mechanics, as well as some remarks of a historical nature. To keep the discussion focussed, most of the paper is confined to equations of “rigid body”,...
Stress-Energy-Momentum Tensors (1992)
We present a new method of constructing a stress-energy-momentum tensor for a classical field theory based on covariance considerations and Noether theory. The stress-energy-momentum tensor # that we...
Cálculo vectorial / J.E. Marsden, Anthony J. Tromba; tr. por Manuel López Mateos. (1991)
Marsden, Jerrold E., Tromba, Anthony J.
Traducción de: Vector calculus
Cálculo vectorial / Jerrold E. Marsden, Anthony J. Tromba (1991)
Marsden, Jerrold E, Tromba, Anthony J
Traducción de: Vector calculus
Exponentially small estimate for separatrix splittings (1991)
Jürgen Scheurle, Jerrold E. Marsden, Philip Holmes
ABSTRACT This paper reviews our previous estimates and gives an example exhibiting a new phenomenon. In problems involving asymptotics beyond all orders in a perturbation parameter ε, it is a common...
Preserving Symplectic Integrator, George Patrick, George Patrick, Jerrold E. Marsden
The dynamics of two rigid bodies coupled by an ideal spherically symmetric joint is studied. Except for preliminary material, attention is restricted to the case of two identical bodies with two...
Reduction, symmetry and phases in mechanics / J. E. Marsden, R. Montgomery and T. Ratiu (1990)
Marsden, Jerrold E, Ratiu, Tudor S
November 1990volume 88number 436 first of 2 number
Stabilization of Rigid Body Dynamics by Internal and External Torques (1990)
Bloch, Anthony M., Krishnaprasad, P.S., Marsden, Jerrold E.
In this paper we discuss the stabilization of the rigid body dynamics by external torques (gas jets) and internal torques (momentum wheels). We compare the stabilizing quadratic quadratic feedback...
Stabilization of Rigid Body Dynamics by Internal and External Torques (1990)
Bloch, Anthony M., Krishnaprasad, P.S., Marsden, Jerrold E.
In this paper we discuss the stabilization of the rigid body dynamics by external torques (gas jets) and internal torques (momentum wheels). We compare the stabilizing quadratic quadratic feedback...
Normalizing connections and the energy-momentum method (1990)
Lewis, Debra, Marsden, Jerrold E., Ratiu, Tudor S., Simo, J. C.
Marsden, Jerrold E, American Mathematical Society, ...
Incluye bibliografía
Manifolds tensor analysis and applications / R. Abraham, J.E. Marsden, T. Ratiu (1988)
Abraham, Ralph, Marsden, Jerrold E, Ratiu, Tudor S
Incluye bibliografía e índice
Foundations of Mechanics, Second Edition (1987)
Abraham, Ralph, Marsden, Jerrold E.
Preface to the Second Edition Since the first edition of this book appeared in 1967, there has been a great deal of activity in the field of symplectic geometry and Hamiltonian systems. In addition...
Nonlinear stability analysis of stratified fluid equilibria (1986)
Abarbanel, Henry D. I., Holm, Darryl D., Marsden, Jerrold E., Ratiu, Tudor S.
The Hamiltonian structure for dynamic free boundary problems (1986)
Lewis, Debra, Marsden, Jerrold E., Montgomery, Richard, Ratiu, Tudor S.
Reduction of Poisson manifolds (1986)
Jerrold E. Marsden, Tudor Ratiu
Reduction in the category of Poisson manifolds is defined and some basic properties are derived. The context is chosen to include the usual theorems on reduction of symplectic manifolds, as well as...
Student's guide to calculus / by J. Marsden and A. Wiestein (1985)
Soon, Frederick H, Marsden, Jerrold E.
Guide to Marsden and Weisntein's Calculus II
Calculus / Jerrold Marsden, Alan Weinstein (1985)
Marsden, Jerrold E, Weinstein, Alan
Incluye índice
Marsden, Jerrold E., Weinstein, Alan
Preface: The goal of this text is to help students learn to use calculus intelligently for solving a wide variety of mathematical and physical problems. This book is an outgrowth of our teaching of...
Marsden, Jerrold E., Weinstein, Alan
Preface: The goal of this text is to help students learn to use calculus intelligently for solving a wide variety of mathematical and physical problems. This book is an outgrowth of our teaching of...
Marsden, Jerrold E., Weinstein, Alan
Preface: The goal of this text is to help students learn to use calculus intelligently for solving a wide variety of mathematical and physical problems. This book is an outgrowth of our teaching of...
Nonlinear stability of fluid and plasma equilibria (1985)
Holm, Darryl D., Marsden, Jerrold E., Ratiu, Tudor S., Weinstein, Alan
Arnold diffusion in the swing equations of a power system (1984)
Salam, Fathi M. A., Marsden, Jerrold E., Varaiya, Pravin P.
We present an application of the theory of Arnold diffusion to interconnected power systems. Using a Hamiltonian formulation, we show that Arnold diffusion arises on certain energy levels of the...
Richardson Number Criterion for the Nonlinear Stability of Three-Dimensional Stratified Flow (1984)
Abarbanel, Henry D. I., Holm, Darryl D., Marsden, Jerrold E., Ratiu, Tudor
With use of a method of Arnol'd, we derive the necessary and sufficient conditions for the formal stability of a parallel shear flow in a three-dimensional stratified fluid. When the local Richardson...
Richardson number criterion for the nonlinear stability of three-dimensional stratified flow (1984)
Abarbanel, Henry D. I., Holm, Darryl D., Marsden, Jerrold E., Ratiu, Tudor
With use of a method of Arnol'd, we derive the necessary and sufficient conditions for the formal stability of a parallel shear flow in a three-dimensional stratified fluid. When the local Richardson...
Stability of rigid body motion using the energy-Casimir method (1984)
Holm, Darryl D., Marsden, Jerrold E., Ratiu, Tudor S., Weinstein, Alan
Richardson number criterion for the nonlinear stability of three-dimensional stratified flow (1984)
Abarbanel, Henry D. I., Holm, Darryl D., Marsden, Jerrold E., Ratiu, Tudor S.
Examples for the Infinite Dimensional Morse Lemma (1983)
Buchner, Michael, Marsden, Jerrold E., Schechter, Stephen
Examples are presented which show how to use the Morse lemma in specific infinite dimensional examples and what can go wrong if various hypotheses are dropped. One of the examples shows that the...
Chaos and Arnold diffusion in dynamical systems (1983)
Salam, Fathi M. A., Marsden, Jerrold E., Varaiya, Pravin P.
Chaotic motion refers to complicated trajectories in dynamical systems. It occurs even in deterministic systems governed by simple differential equations and its presence has been experimentally...
Mathematical Foundations of Elasticity (1983)
Marsden, Jerrold E., Hughes, Thomas J.R.
Libro de fundamentos matemáticos de la elasticidad. Contenido: Geometría y cinemática de los cuerpos; Principios de equilibrio; Teoría constitutiva; Linearización; Principios hamiltonianos y...
Mathematical Foundations of Elasticity / J.E. Marsden, T.J.R. Hughes. (1983)
Marsden, Jerrold E., Hughes, Thomas J.R.
Libro de fundamentos matemáticos de la elasticidad. Contenido: Geometría y cinemática de los cuerpos; Principios de equilibrio; Teoría constitutiva; Linearización; Principios hamiltonianos y...
Hamiltonian systems with symmetry, coadjoint orbits and plasma physics (1983)
Marsden, Jerrold E., Weinstein, Alan, Ratiu, Tudor S., Schmid, Rudolf, Spencer, R. G.
Nonlinear stability conditions and a priori estimates for barotropic hydrodynamics (1983)
Holm, Darryl D., Marsden, Jerrold E., Ratiu, Tudor S., Weinstein, Alan
Melnikov's method and Arnold diffusion for perturbations of integrable Hamiltonian systems (1982)
Holmes, Philip J., Marsden, Jerrold E.
We start with an unperturbed system containing a homoclinic orbit and at least two families of periodic orbits associated with action angle coordinates. We use Kolmogorov–Arnold–Moser (KAM)...
Marsden, Jerrold E, Tromba, Anthony
Traducción de: Vector calculus
Cálculo vectorial / Jerrold E. Marsden, Anthony J. Tromba (1981)
Marsden, Jerrold E, Tromba, Anthony J
Traducción de: Vector calculus
Philip Holmes, Jerrold E. Marsden
This paper delineates a class of time-periodically perturved evolution equations in a Banach space whose associated Poincaré map contains a Smale horseshoe. This implies that such systems possess...
Kaiser, Gerald, Marsden, Jerrold E
Incluye bibliografía
Abraham, Ralph, Marsden, Jerrold E
"A mathematical exposition of classical mechanics with an introduction to the qualitative theory of dynamical systems and applications to the three-body problem"
Eitan Grinspun, Committee Alan Barr, Mathieu Desbrun, Jerrold E. Marsden, Petr Krysl
THESIS CHARMS (Conforming Hierarchical Adaptive Refinement Methods) is an adaptive simulation technology that spans the spectrum from real-time animation for games, realistic animation for film, to...
Applications of global analysis in mathematical physics (1974)
These notes are based on a series of ten lectures given at Carleton University, Ottawa, from June 21 through July 6, 1973. The notes follow the lectures fairly closely except for a few minor...
The Einstein Equations of Evolution - A Geometric Approach (1972)
Fischer, A. E., Marsden, Jerrold E.
In this paper the exterior Einstein equations are explored from a differential geometric point of view. Using methods of global analysis and infinite-dimensional geometry, we answer sharply the...
The Einstein evolution equations as a first-order quasi-linear symmetric hyperbolic system. I (1972)
Lectures on analysis / Gustave Choquet (1969)
Choquet, Gustave, Marsden, Jerrold E, Lance, T. (Tim)
"This book is an expansion and revision of lecture notes from Professor Choquet's course in analysis given at Princeton during the fall term in 1967"
Hamiltonian one parameter groups and generalized Hamiltonian mechanics. (1968)
Thesis (Ph. D.)--Princeton.
Cálculo Vectorial / J.E. Marsden ; tr. por Manuel López Mateos. (1968)
Marsden, Jerrold E., Tromba, Anthony J.
Traducción de: Vector Calculos
Abstract mechanical connection and abelian reconstruction for almost Kähler manifolds
Pekarsky, Sergey, Marsden, Jerrold E.
When the phase space $P$ of a Hamiltonian $G$-system $(P,\omega,G,J,H)$ has an almost Kähler structure a preferred connection, called abstract mechanical connection, can be defined by declaring...
Matching and stabilization of discrete mechanical systems
Bloch, Anthony M., Leok, Melvin, Marsden, Jerrold E., Zenkov, Dmitry V.
Controlled Lagrangian and matching techniques are developed for the stabilization of equilibria of discrete mechanical systems with symmetry as well as broken symmetry. Interesting new phenomena...
Multisymplectic Geometry, Variational Integrators, and Nonlinear PDEs
Jerrold E. Marsden, George W. Patrick, Steve Shkoller
This paper presents a geometric-variational approach to continuous and discrete mechanics and field theories. Using multisymplectic geometry, we show that the existence of the fundamental geometric...