Variational calculus with constraints on general algebroids

Details Variational calculus with constraints on general algebroids Variational calculus with constraints on general algebroids

2007-12-17

arxiv.org/abs/0712.2766v2

J. Phys. A: Math. Theor. 41 (2008), 175204

Physics

Mathematical Physics

23 pages, a few references added, the version to appear in J. Phys. A: Math. Theor

Scientific paper

10.1088/1751-8113/41/17/175204

Variational calculus on a vector bundle E equipped with a structure of a general algebroid is developed, together with the corresponding analogs of Euler-Lagrange equations. Constrained systems are introduced in the variational and in the geometrical setting. The constrained Euler-Lagrange equations are derived for analogs of holonomic, vakonomic and nonholonomic constraints. This general model covers majority of first-order Lagrangian systems which are present in the literature and reduces to the standard variational calculus and the Euler-Lagrange equations in Classical Mechanics for E=TM.

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