%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.}, biburl = {https://www.bibsonomy.org/bibtex/289bad03b1d85fd1fc129737c0e54fb95/drmatusek}, doi = {10.1098/rspa.2011.0158}, groups = {public}, interhash = {3ce8d94bf8df54779069d93342e1195d}, intrahash = {89bad03b1d85fd1fc129737c0e54fb95}, 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 }