Dirac Structures and Hamilton-Jacobi Theory for Lagrangian Mechanics on   Lie Algebroids
  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. 
Melvin Leok, Diana Sosa
math-ph math.MP