Invariant Measures of Nonholonomic Flows with Internal Degrees of Freedom
نویسندگان
چکیده
In this paper we study measure preserving flows associated with nonholonomic systems with internal degrees of freedom. Our approach reveals geometric reasons for existence of measures in the form of an integral invariant with smooth density that depends on the internal configuration of the system.
منابع مشابه
ar X iv : m at h - ph / 0 30 70 16 v 1 8 J ul 2 00 3 Nonholonomic LR systems as Generalized Chaplygin systems with an Invariant Measure and Geodesic Flows on Homogeneous Spaces ∗
We consider a class of dynamical systems on a Lie group G with a leftinvariant metric and right-invariant nonholonomic constraints (so called LR systems) and show that, under a generic condition on the constraints, such systems can be regarded as generalized Chaplygin systems on the principle bundle G → Q = G/H , H being a Lie subgroup. In contrast to generic Chaplygin systems, the reductions o...
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