Hamiltonization of Nonholonomic Systems and the Inverse Problem of the Calculus of Variations

TL;DR

This paper presents a method to transform certain nonholonomic systems into unconstrained Hamiltonian systems on the full phase space, facilitating analysis and control design.

Contribution

It introduces a novel Hamiltonization technique for nonholonomic systems via the inverse calculus of variations, linking it to the Pontryagin maximum principle.

Findings

Method successfully recovers equations of motion for nonholonomic systems.

Illustrated with multiple examples demonstrating effectiveness.

Establishes a connection between Hamiltonization and optimal control principles.

Abstract

We introduce a method which allows one to recover the equations of motion of a class of nonholonomic systems by finding instead an unconstrained Hamiltonian system on the full phase space, and to restrict the resulting canonical equations to an appropriate submanifold of phase space. We focus first on the Lagrangian picture of the method and deduce the corresponding Hamiltonian from the Legendre transformation. We illustrate the method with several examples and we discuss its relationship to the Pontryagin maximum principle.