Extensions of Noether's Second Theorem: from continuous to discrete systems
P. Hydon, и E. Mansfield. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 467 (2135):
3206-3221(ноября 2011)
DOI: 10.1098/rspa.2011.0158
Аннотация
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.
%0 Journal Article
%1 10.1098/rspa.2011.0158
%A Hydon, Peter E.
%A Mansfield, Elizabeth L.
%D 2011
%J Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
%K ODEs classical mathematics mechanics physics symmetry variational
%N 2135
%P 3206-3221
%R 10.1098/rspa.2011.0158
%T Extensions of Noether's Second Theorem: from continuous to discrete systems
%V 467
%X 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.
@article{10.1098/rspa.2011.0158,
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 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.},
added-at = {2011-10-03T17:24:05.000+0200},
author = {Hydon, Peter E. and Mansfield, Elizabeth L.},
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journal = {Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences},
keywords = {ODEs classical mathematics mechanics physics symmetry variational},
month = {November},
number = 2135,
pages = {3206-3221},
timestamp = {2013-05-03T12:42:45.000+0200},
title = {Extensions of Noether's Second Theorem: from continuous to discrete systems},
username = {drmatusek},
volume = 467,
year = 2011
}