Pseudo-symmetries, Noether's theorem and the adjoint equation
- 21 April 1987
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 20 (6) , 1365-1376
- https://doi.org/10.1088/0305-4470/20/6/020
Abstract
Pseudo-symmetries were introduced by Sarlet and Cantrijn (1984) for time-dependent non-conservative systems. They are reconsidered in the context of general autonomous second-order systems, relying on the new approach to such systems which was presented by Sarlet et al. They further introduce the notion of adjoint symmetries of a second-order system, as being associated to invariant 1-forms, and show how they may be related to first integrals or to Lagrangians under appropriate circumstances. Their results enable them to clarify a rather unusual account of Noether's theorem which was recently given by Gordon (1986).Keywords
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