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

By Peter E. Hydon and Elizabeth L. Mansfield


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 on 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

Topics: QA299, QA297, QA252
Publisher: Royal Society
Year: 2011
OAI identifier: oai:kar.kent.ac.uk:27986
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