Impulsive control of a symmetric ball rolling without sliding orspinning

Hernán Cendra; María Etchechoury; Sebastián J. Ferraro

doi:10.3934/jgm.2010.2.321

Article Contents

2010, Volume 2, Issue 4: 321-342. Doi: 10.3934/jgm.2010.2.321

This issue Previous Article Next Article Variational integrators for discrete Lagrange problems

Impulsive control of a symmetric ball rolling without sliding or spinning

1.
Departamento de Matemática, Universidad Nacional del Sur, Av. Alem 1253, 8000 Bahía Blanca and CONICET
2.
Laboratorio de Electrónica Industrial, Control e Instrumentación, Facultad de Ingeniería, Universidad Nacional de La Plata and Departamento de Matemática, Facultad de Ciencias Exactas, Universidad Nacional de La Plata., CC 172, 1900 La Plata
3.
Departamento de Mateemática and Instituto de Matemática Bahía Blanca, Universidad Nacional del Sur, Av. Alem 1253, 8000 Bahía Blanca and CONICET

Received: May 2010

Revised: December 2010

Published: December 2010

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Abstract

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 $S^2 \times S^1$. 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.

Keywords:

Nonholonomic systems; control; geometric mechanics.

Mathematics Subject Classification: 70F25, 70Q05, 49N25.

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