Virial theorem in quasi-coordinates and Lie algebroid formalism

TL;DR

This paper extends the geometric virial theorem to systems described by quasi-coordinates and Lie algebroids, providing a unified framework for analyzing mechanical systems with complex geometric structures.

Contribution

It generalizes the virial theorem to Lie algebroid settings using geometric methods, incorporating quasi-velocities for broader applicability.

Findings

Derived a generalized virial theorem for Lie algebroid systems.

Unified geometric framework for quasi-coordinates and Lie algebroids.

Extended previous approaches to more complex geometric structures.

Abstract

In this paper, the geometric approach to the virial theorem developed in \cite{CFR12} is written in terms of quasi-velocities (see \cite{CNCS07}). A generalization of the virial theorem for mechanical systems on Lie algebroids is also given, using the geometric tools of Lagrangian and Hamiltonian mechanics on the prolongation of the Lie algebroid.