Exterior differential systems on Lie algebroids and the invariant inverse problem of the calculus of variations

Abstract

We extend the theory of exterior differential systems from manifolds and their tangent bundles to Lie algebroids. In particular, we define the concept of an integral manifold of such an exterior differential system. We support our developments with several examples, including an application to dynamical systems with a symmetry group and to the invariant inverse problem of the calculus of variations.

arXiv comment37 pages

References in corpus (6)

• Lagrangian submanifolds and dynamics on Lie algebroids
• Lie algebroid structures and Lagrangian systems on affine bundles
• Lagrange-Poincare field equations
• Reduction and reconstruction aspects of second-order dynamical systems with symmetry
• Invariant Lagrangians, mechanical connections and the Lagrange-Poincare equations
• New progress in the inverse problem in the calculus of variations