Variational Constrained Mechanics on Lie Affgebroids

TL;DR

This paper develops a variational framework for constrained mechanics on Lie affgebroids, deriving dynamical equations and Poisson brackets, with special focus on affine constraints and practical examples.

Contribution

It introduces a novel variational approach to vakonomic mechanics on Lie affgebroids, including new equations and brackets for affine constraints.

Findings

Derived dynamical equations for vakonomic systems on Lie affgebroids

Established the aff-Poisson bracket structure for these systems

Applied the theory to multiple illustrative examples

Abstract

In this paper we discuss variational constrained mechanics (vakonomic mechanics) on Lie affgebroids. We obtain the dynamical equations and the aff-Poisson bracket associated with a vakonomic system on a Lie affgebroid ${\mathcal A}$. We devote special attention to the particular case when the nonholonomic constraints are given by an affine subbundle of ${\mathcal A}$ and we discuss the variational character of the theory. Finally, we apply the results obtained to several examples.