Noether's theorem for the variational equations

Details Noether's theorem for the variational equations Noether's theorem for the variational equations

2004-02-23

arxiv.org/abs/math-ph/0402062v1

Physics

Mathematical Physics

5 pages, no figures, a slightly different published version exists

Scientific paper

We introduce an generalized action functional describing the equations of motion and the variational equations for any Lagrangian system. Using this novel scheme we are able to generalize Noether's theorem in such a way that to any $n$-parameter continuous symmetry group of the Lagrangian there exist 1) the usual $n$ constants of motion and 2) $n$ extra constants valid in the variational equations. The new constants are related to the infinitesimal generators of the symmetry transformation by relations similar to the ones that stem from the `nonextended' Noether theorem.

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