Journal
INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS
Volume 3, Issue 7, Pages 1417-1458Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0219887806001764
Keywords
Hamilton-Jacobi equation; Lagrangian system; Hamiltonian system; singular dynamics; alternative Lagrangians
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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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