Reducción de Routh, mecánica de Cartan y cuasicoordenadas

CAPRIOTTI, SANTIAGO

Valparaíso

Encuentro; Sesión invitada: Teoría espectral y métodos geométricos en el Primer Encuentro Conjunto de la Sociedad de Matemática de Chile y la Unión Matemática Argentina (SUMA); 2016

Universidad de Valparaíso, Pontificia Universidad Católica de Valparaíso, Universidad Técnica Federico Santa María

Routh reduction is a procedure, in the Lagrangian setting, analogous to the Marsden-Weinstein reduction. It is based on the fact that, because solutions of Euler-Lagrange equations are contained in the level sets of the momentum map, reduction can be carried out in one of these level sets, provided it has a manifold structure. On the other hand, Cartan mechanics is a geometrical formulation for classical mechanics designed to work with time-dependent Lagrangian systems. In the present talk we will discuss how to generalize Routh reduction construction to the Cartan mechanics realm. As a byproduct, we will be able to write out the equations of motion in quasicoordinates, allowing us to compare our results with other approaches to the problem that can be found in literature.