Generalized Livens theorem and constrained Hamiltonian dynamics on algebroids

TL;DR

This paper extends Livens theorem to algebroids, providing a variational principle-based approach to Hamiltonian dynamics, including constrained systems, on vector bundles dual to algebroids.

Contribution

It generalizes Livens theorem to algebroids and introduces a variational principle framework for Hamiltonian dynamics with constraints on these structures.

Findings

Hamiltonian equations derived via variational principle on algebroids.

Framework applicable to constrained Hamiltonian systems, including nonholonomic constraints.

Extension of classical results to a broader geometric setting.

Abstract

We generalise Livens theorem, showing that Hamiltonian equation on the vector bundle $E^\ast\rightarrow M$, dual to a general algebroid $E\rightarrow M$, can be derived by means of a variational principle. The framework can be used to describe Hamiltonian dynamics associated with (both vaconomic and nonholonomic) constraints in the bundle $E$.