Affine Generalizations of the Nonholonomic Problem of a Convex Body Rolling without Slipping on the Plane
Author(s):
Costa-Villegas M., García-Naranjo L. C.
We introduce a class of examples which provide an affine generalization of the
nonholonomic problem of a convex body that rolls without slipping on the plane. These examples
are constructed by taking as given two vector fields, one on the surface of the body and another
on the plane, which specify the velocity of the contact point. We investigate dynamical aspects
of the system such as existence of first integrals, smooth invariant measure, integrability and
chaotic behavior, giving special attention to special shapes of the convex body and specific
choices of the vector fields for which the affine nonholonomic constraints may be physically
realized.
Keywords:
nonholonomic systems, rigid body dynamics, first integrals, invariant measure, integrability, chaotic behavior
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