The Lagrange-d'Alembert-Poincare Equations for the Symmetric Rolling Sphere

Hernan Cendra, Universidad Nacional del Sur, Av. Alem 1254, 8000 Bahia Blanca and CONICET, Argentina, Departamento de Matematica

Nonholonomic systems are described by the Lagrange-d'Alembert principle. The presence of symmetry leads, upon the choice of an arbitrary principal connection, to a reduced variational principle and to the Lagrange-d'Alembert-Poincare reduced equations. The case of rolling constraints has a long history and it has been the purpose of many works in recent times, in part because of its applications to robotics. In this paper we study the case of a symmetric sphere, that is, a sphere where two of its three moments of inertia are equal, rolling on a plane, using an abelian group of symmetry. The presence of some impulsive constraints and its effect on the reduced variables is also briefly studied.