Jorge Cortés
Professor
Cymer Corporation Endowed Chair
Mechanical control systems on Lie algebroids
J. Cortés, E. Martínez
IMA Journal of Mathematical Control and Information 21 (4) (2004), 457-492
Abstract
This paper considers control systems defined on Lie algebroids. After
deriving basic controllability tests for general control systems, we
specialize our discussion to the class of mechanical control systems
on Lie algebroids. This class of systems includes mechanical systems
subject to holonomic and nonholonomic constraints, mechanical systems
with symmetry and mechanical systems evolving on semidirect
products. We introduce the notions of linear connection, symmetric
product and geodesically invariant subbundle on a Lie algebroid. We
present appropriate tests for various notions of accessibility and
controllability, and analyze the relation between the controllability
properties of control systems related by a morphism of Lie algebroids.
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