Non-holonomic Lagrangian systems on Lie algebroids

Abstract

This paper presents a geometric description on Lie algebroids of Lagrangian systems subject to nonholonomic constraints. The Lie algebroid framework provides a natural generalization of classical tangent bundle geometry. We define the notion of nonholonomically constrained system, and characterize regularity conditions that guarantee the dynamics of the system can be obtained as a suitable projection of the unconstrained dynamics. The proposed novel formalism provides new insights into the geometry of nonholonomic systems, and allows us to treat in a unified way a variety of situations, including systems with symmetry, morphisms and reduction, and nonlinearly constrained systems. Various examples illustrate the results.

To appear in Discrete and Continuous Dynamical Systems - A

References in corpus (1)

• Nonholonomic LR systems as Generalized Chaplygin systems with an Invariant Measure and Geodesic Flows on Homogeneous Spaces

Cited by in corpus (6)

• Discrete Nonholonomic Lagrangian Systems on Lie Groupoids
• Lie Algebroids in Classical Mechanics and Optimal Control
• A general framework for nonholonomic mechanics: Nonholonomic Systems on Lie affgebroids
• Gauge equivalence and conserved quantities for Lagrangian systems on Lie algebroids
• Variational calculus on Lie algebroids
• Limites projectives fortes d'algébroïdes de Lie