Geometrical Mechanics on algebroids

Details Geometrical Mechanics on algebroids Geometrical Mechanics on algebroids

2005-09-27

arxiv.org/abs/math-ph/0509063v2

Int. J. Geom. Meth. Mod. Phys. 3 (2006), 559-575.

Physics

Mathematical Physics

13 pages, minor changes, the version to appear in Int. J. Geom. Meth. Mod. Phys

Scientific paper

A natural geometric framework is proposed, based on ideas of W. M. Tulczyjew, for constructions of dynamics on general algebroids. One obtains formalisms similar to the Lagrangian and the Hamiltonian ones. In contrast with recently studied concepts of Analytical Mechanics on Lie algebroids, this approach requires much less than the presence of a Lie algebroid structure on a vector bundle, but it still reproduces the main features of the Analytical Mechanics, like the Euler-Lagrange-type equations, the correspondence between the Lagrangian and Hamiltonian functions (Legendre transform) in the hyperregular cases, and a version of the Noether Theorem. Besides, the constructions seem to be more natural and simpler.

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