A Survey of Lagrangian Mechanics and Control on Lie algebroids and groupoids
Jorge Cortes, Manuel de Leon, Juan C. Marrero, D. Martin de Diego and, Eduardo Martinez
TL;DR
This survey reviews the geometric framework of Lagrangian and Hamiltonian mechanics on Lie algebroids, highlighting its versatility in handling constrained systems, control, discrete mechanics, and field theories with illustrative examples.
Contribution
It provides a comprehensive geometric overview of mechanics on Lie algebroids, unifying various extensions and applications within a single formalism.
Findings
Effective analysis of nonholonomic constraints
Unified treatment of control and discrete mechanics
Illustrative examples demonstrating the approach
Abstract
In this survey, we present a geometric description of Lagrangian and Hamiltonian Mechanics on Lie algebroids. The flexibility of the Lie algebroid formalism allows us to analyze systems subject to nonholonomic constraints, mechanical control systems, Discrete Mechanics and extensions to Classical Field Theory within a single framework. Various examples along the discussion illustrate the soundness of the approach.
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Taxonomy
TopicsControl and Dynamics of Mobile Robots · Homotopy and Cohomology in Algebraic Topology · Nonlinear Waves and Solitons