Euler-Poincaré equations by several stages

VIVIANA A. DÍAZ

Santiago de Compostela

Congreso; IV International Summer School on Geometry, Mechanics and Control; 2010

Universidad de Santiago de Compostela

Euler-Poincaré equations by several stages. The reduction of the Euler-Lagrange equations by means of reduction of Hamilton's principle using a geometric point of view gives rise to the Euler-Poincaré equations. In the case in which the group has a chain of normal subgroups, the decomposition of the Lie algebra and the resulting expression for the Lie bracket lead to a decomposition by stages of the Euler-Poincaré equations. Our aim is to show explicit expression of the Euler-Poincaré equations by several stages in terms of a given principal connection. References: - Cendra, H., Marsden, J. and Ratiu, T. Lagrangian Reduction by Stages, Memoirs of the American Mathematical Society, Volume 152, Number 722, 2001. - Cendra, H. and Díaz, V.A. Lagrange-d'Alembert-Poincaré equations by several stages, to appear.