A Generalization of Chaplygin's Reducibility Theorem (2009)
Fernandez, O. E., Mestdag, T., Bloch, A. M.
In this paper we study Chaplygin's Reducibility Theorem and extend its applicability to nonholonomic systems with symmetry described by the Hamilton-Poincare-d'Alembert equations in arbitrary degrees...
Keywords: Stabilization of Non-linear Systems, Dissipative (2008)
C. A. Woolsey, A. M. Bloch, N. E. Leonard, J. E. Marsden
We describe the effect of physical dissipation on stability of equilibria which have been stabilized, in the absence of damping, using the method of controlled Lagrangians. This method applies to a...
Hamiltonization of Nonholonomic Systems and the Inverse Problem of the Calculus of Variations (2008)
Bloch, A. M., Fernandez, O. E., Mestdag, T.
We introduce a method which allows one to recover the equations of motion of a class of nonholonomic systems by finding instead an unconstrained Hamiltonian system on the full phase space, and to...
Dissipation and controlled Euler-Poincaré systems (2001)
C. A. Woolsey, A. M. Bloch, N. E. Leonard, J. E. Marsden
The method of controlled Lagrangians is a technique for stabilizing underactuated mechanical systems which involves modifying a system’s energy and dynamic structure through feedback. These...
Nonholonomic Mechanical Systems with Symmetry (1995)
Bloch, A. M., Krishnaprasad, P. S., Marsden, J. E., Murray, R. 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...