Virial theorem in quasi-coordinates and Lie algebroid formalism

José F. Cariñena, Irina Gheorghiu, Eduardo Mart\'\inez, Patr\'\icia Santos

Published 2014-05-26, updated 2014-05-27Version 2

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.