| Lie Bracket Extensions And Averaging: The Single-Bracket Case (1997) | |||||||||||||||
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| We explain a general approximation technique for nonholonomic systems by discussing in detail a special example, chosen so as to illustrate some of the technical aspects of the general construction. The example considered is that of an extension of a two-input system obtained by adding a single bracket of degree five. This bracket is sufficiently complicated to exhibit some phenomena, such as multiplicity, that do not occur for brackets of lower degree. This author's work was supported in part by the National Science Foundation under NSF Grant DMS-8902994. INTRODUCTION In [19], we introduced a general approximation technique for nonholonomic systems which gives an explicit construction, for any given path fl in state space, of a sequence of admissible trajectories converging to fl, and in addition has a number of other desirable properties. The technique is based on an improved version of a theorem proved by Haynes and Hermes in [5], and uses a result on convergence of trajectorie... | |||||||||||||||
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