A Lie algebroid framework for non-holonomic systems

Abstract

In order to obtain a framework in which both non-holonomic mechanical systems and non-holonomic mechanical systems with symmetry can be described, we introduce in this paper the notion of a Lagrangian system on a subbundle of a Lie algebroid.

18 pages

References in corpus (2)

• Lie algebroid structures and Lagrangian systems on affine bundles
• The Berwald-type linearisation of generalised connections

Cited by in corpus (8)

• Lagrangian submanifolds and dynamics on Lie algebroids
• A unified framework for mechanics. Hamilton-Jacobi equation and applications
• Geometric Hamilton-Jacobi Theory for Nonholonomic Dynamical Systems
• Discrete Nonholonomic Lagrangian Systems on Lie Groupoids
• Anholonomic frames in constrained dynamics
• Symmetries of second order differential equations on Lie algebroids
• A general framework for nonholonomic mechanics: Nonholonomic Systems on Lie affgebroids
• Reduction of invariant constrained systems using anholonomic frames