The Hojman Construction and Hamiltonization of Nonholonomic Systems

TL;DR

This paper explores the Hojman construction to generate Poisson brackets for nonholonomic systems, revealing new structures that often lack invariant measures and Casimir functions, thus broadening the understanding of Hamiltonization in such systems.

Contribution

It introduces novel Poisson brackets derived via the Hojman construction that differ from traditional Hamiltonian structures in nonholonomic mechanics.

Findings

Poisson brackets with nonmaximal rank are constructed.

Invariant measures and Casimir functions may be absent.

Examples demonstrate the diversity of Hamiltonian structures in nonholonomic systems.

Abstract

In this paper, using the Hojman construction, we give examples of various Poisson brackets which differ from those which are usually analyzed in Hamiltonian mechanics. They possess a nonmaximal rank, and in the general case an invariant measure and Casimir functions can be globally absent for them.