The Journal of Geometric Mechanics (JGM)

When is a control system mechanical?

Pages: 265 - 302, Volume 2, Issue 3, September 2010      doi:10.3934/jgm.2010.2.265

       Abstract        References        Full Text (647.8K)       Related Articles

Sandra Ricardo - Department of Mathematics, School of Sciences and Technology, University of Trás-os-Montes e Alto Douro, 5001-801 Vila Real, Portugal (email)
Witold Respondek - INSA-Rouen, Laboratoire de Mathématiques, 76801 Saint-Etienne-du-Rouvray, France (email)

Abstract: In this work we present a geometric setting for studying mechanical control systems. We distinguish a special class: the class of geodesically accessible mechanical systems, for which the uniqueness of the mechanical structure is guaranteed (up to an extended point transformation). We characterise nonlinear control systems that are state equivalent to a system from this class and we describe the canonical mechanical structure attached to them. Several illustrative examples are given.

Keywords:  Mechanical control systems, state equivalence, mechanical state equivalence, geodesic accessibility, symmetric product.
Mathematics Subject Classification:  Primary: 53Bxx, 93Cxx; Secondary: 37Jxx.

Received: May 2010;      Available Online: November 2010.