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arXiv · 1103.3267

Extensions of Noether's Second Theorem: from continuous to discrete systems

Peter E. Hydon·Elizabeth L. Mansfield
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Abstract

A simple local proof of Noether's Second Theorem is given. This proof immediately leads to a generalization of the theorem, yielding conservation laws and/or explicit relationships between the Euler--Lagrange equations of any variational problem whose symmetries depend upon a set of free or partly-constrained functions. Our approach extends further to deal with finite difference systems. The results are easy to apply; several well-known continuous and discrete systems are used as illustrations.

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Peter E. Hydon, Elizabeth L. Mansfield. 2011-03-09. Extensions of Noether's Second Theorem: from continuous to discrete systems. https://doi.org/10.1098/rspa.2011.0158

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