Journal
INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS
Volume 3, Issue 3, Pages 559-575Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0219887806001259
Keywords
Lie algebroid; double vector bundle; Lagrangian function; Euler-Lagrange equations
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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.
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