Nonholonomic constraints in $k$-symplectic Classical Field Theories

Details Nonholonomic constraints in $k$-symplectic Classical Field Theories Nonholonomic constraints in $k$-symplectic Classical Field Theories

2008-03-11

arxiv.org/abs/0803.1540v1

Int.J.Geom.Meth.Mod.Phys.05:799-830,2008

Physics

Mathematical Physics

27 pages

Scientific paper

10.1142/S0219887808003077

A $k$-symplectic framework for classical field theories subject to nonholonomic constraints is presented. If the constrained problem is regular one can construct a projection operator such that the solutions of the constrained problem are obtained by projecting the solutions of the free problem. Symmetries for the nonholonomic system are introduced and we show that for every such symmetry, there exist a nonholonomic momentum equation. The proposed formalism permits to introduce in a simple way many tools of nonholonomic mechanics to nonholonomic field theories.

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