Singular lagrangian systems and variational constrained mechanics on Lie algebroids

TL;DR

This paper develops a framework for Lagrangian mechanics on Lie algebroids, addressing singular systems and vakonomic mechanics, with examples demonstrating its broad applicability to various constrained systems.

Contribution

It introduces a unified approach to constrained Lagrangian mechanics on Lie algebroids, including singular and vakonomic cases, expanding the theoretical foundation and practical applications.

Findings

Framework covers systems on Lie groups and quotients

Addresses singular Lagrangian systems and vakonomic mechanics

Includes illustrative examples demonstrating applicability

Abstract

The purpose of this paper is describe Lagrangian Mechanics for constrained systems on Lie algebroids, a natural framework which covers a wide range of situations (systems on Lie groups, quotients by the action of a Lie group, standard tangent bundles...). In particular, we are interested in two cases: singular Lagrangian systems and vakonomic mechanics (variational constrained mechanics). Several examples illustrate the interest of these developments.