Hamiltonization and geometric integration of nonholonomic mechanical systems

TL;DR

This paper develops a Hamiltonization method for nonholonomic mechanical systems, enabling the use of variational integrators and improving geometric integration techniques for systems with velocity-dependent constraints.

Contribution

It introduces a Hamiltonization approach that reformulates nonholonomic systems as Euler-Lagrange equations and applies this to compare variational and nonholonomic integrators.

Findings

Hamiltonization transforms nonholonomic systems into Hamiltonian form.

Comparison shows variational integrators perform well for the new Lagrangians.

Provides a framework for geometric integration of nonholonomic systems.

Abstract

In this paper we study a Hamiltonization procedure for mechanical systems with velocity-depending (nonholonomic) constraints. We first rewrite the nonholonomic equations of motion as Euler-Lagrange equations, with a Lagrangian that follows from rephrasing the issue in terms of the inverse problem of Lagrangian mechanics. Second, the Legendre transformation transforms the Lagrangian in the sought-for Hamiltonian. As an application, we compare some variational integrators for the new Lagrangians with some known nonholonomic integrators.