Leok, MelvinSosa Martín, Diana Nieves2015-06-252015-06-252012Leok, M., & Sosa, D. (2012). Dirac structures and Hamilton-Jacobi theory for Lagrangian mechanics on lie algebroids. The Journal of Geometric Mechanics (JGM), 4(4), 441-442.1941488919414897http://hdl.handle.net/11268/4153This 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 TEE∗. This setting includes degenerate Lagrangian systems with nonholonomic constraints on Lie algebroids.engDirac structuresImplicit Lagrangian systemsLie algebroidsLagrangian mechanicsNonholonomic systemsHamilton-Jacobi equationjournal article10.3934/jgm.2012.4.421restricted accessÁlgebraMatemáticasÁlgebraMatemáticasCiencia