1211.4561 (Melvin Leok et al.)

Dirac Structures and Hamilton-Jacobi Theory for Lagrangian Mechanics on
Lie Algebroids    [PDF]

Melvin Leok, Diana Sosa

This paper develops the notion of implicit Lagrangian systems on Lie algebroids and a Hamilton--Jacobi theory for this type of system. The Lie algebroid framework provides a natural generalization of classical tangent bundle geometry. We define the notion of an implicit Lagrangian system on a Lie algebroid $E$ using Dirac structures on the Lie algebroid prolongation $\T^EE^*$. This setting includes degenerate Lagrangian systems with nonholonomic constraints on Lie algebroids.

View original: http://arxiv.org/abs/1211.4561