Geometric Hamilton-Jacobi Theory

Details Geometric Hamilton-Jacobi Theory Geometric Hamilton-Jacobi Theory

2006-04-26

arxiv.org/abs/math-ph/0604063v1

Int.J.Geom.Meth.Mod.Phys.3:1417-1458,2006

Physics

Mathematical Physics

40 pages

Scientific paper

10.1142/S0219887806001764

The Hamilton-Jacobi problem is revisited bearing in mind the consequences arising from a possible bi-Hamiltonian structure. The problem is formulated on the tangent bundle for Lagrangian systems in order to avoid the bias of the existence of a natural symplectic structure on the cotangent bundle. First it is developed for systems described by regular Lagrangians and then extended to systems described by singular Lagrangians with no secondary constraints. We also consider the example of the free relativistic particle, the rigid body and the electron-monopole system.

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