Impulsive control of a symmetric ball rolling without sliding or spinning

HERNÁN CENDRA; MARÍA DEL ROSARIO ETCHECHOURY; SEBASTIÁN J. FERRARO

Journal of Geometric Mechanics

American Institute of Mathematical Sciences

Lugar: Springfield, MO; Año: 2010 vol. 2 p. 321 - 342

1941-4889

A ball having two of its three moments of inertia equal and whose center of mass coincides with its geometric center is called a symmetric ball. The free dynamics of a symmetric ball rolling without sliding or spinning on a horizontal plate has been studied in detail in a previous work by two of the authors, where it was shown that the equations of motion are equivalent to an ODE on the 3-manifold S^2 x S^1. In this paper we present an approach to the impulsive control of the position and orientation of the ball and study the speed of convergence of the algorithm. As an example we apply this approach to the solutions of the isoparallel problem.