Hamiltonization of Elementary Nonholonomic Systems

Abstract

In this paper, we develop the Chaplygin reducing multiplier method; using this method, we obtain a conformally Hamiltonian representation for three nonholonomic systems, namely, for the nonholonomic oscillator, for the Heisenberg system, and for the Chaplygin sleigh. Furthermore, in the case of an oscillator and the nonholonomic Chaplygin sleigh, we show that the problem reduces to the study of motion of a mass point (in a potential field) on a plane and, in the case of the Heisenberg system, on the sphere. Moreover, we consider an example of a nonholonomic system (suggested by Blackall) to which one cannot apply the reducing multiplier method.

References in corpus (5)

• Non-existence of an invariant measure for a homogeneous ellipsoid rolling on the plane
• On the Lie integrability theorem for the Chaplygin ball
• Dynamics of the Tippe Top -- properties of numerical solutions versus the dynamical equations
• On Integrable Perturbations of Some Nonholonomic Systems
• Quaternion Solution for the Rock'n'roller: Box Orbits, Loop Orbits and Recession

Cited by in corpus (5)

• Hamiltonization and separation of variables for Chaplygin ball on a rotating plane
• Infinitesimal time reparametrisation and its applications
• Inverse Jacobi multiplier as a link between conservative systems and Poisson structures
• Reduction of hybrid Hamiltonian systems with non-equivariant momentum maps
• Homogeneous bi-Hamiltonian structures and integrable contact systems