Conserved quantities in the variational equations

C.M. Arizmendi, J. Delgado, H.N. Núñez-Yépez, A.L. Salas-Brito


Noether's theorem relating continuous symmetries of a Lagrangian system to the existence of conserved quantities is shown to be valid at the level of the variational equations of the system. This result can be helpful in the study of perturbations and of integrability in various areas of current interest. As examples, we derive conserved quatities in linearized general relativity and obtain conserved quantities valid in perturbed classical dynamics.


Noether theorem, variational equations, Lagrangian theories

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Revista Mexicana de Física

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