Mansfield, Elizabeth L. and Goncalves, T.M.N.
(2011)
*
On Moving Frames and Noether’s Conservation Laws.
*
Studies in Applied Mathematics,
128
(1).
pp. 1-29.
ISSN 1467-9590.
(doi:10.1111/j.1467-9590.2011.00522.x)
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Official URL http://dx.doi.org/10.1111/j.1467-9590.2011.00522.x |

## Abstract

Noether’s Theorem yields conservation laws for a Lagrangian with a variational symmetry group. The explicit formulae for the laws are well known and the symmetry group is known to act on the linear space generated by the conservation laws. The aim of this paper is to explain the mathematical structure of both the Euler-Lagrange system and the set of conservation laws, in terms of the differential invariants of the group action and a moving frame. For the examples, we demonstrate, knowledge of this structure allows the Euler-Lagrange equations to be integrated with relative ease. Our methods take advantage of recent advances in the theory of moving frames by Fels and Olver, and in the symbolic invariant calculus by Hubert. The results here generalize those appearing in Kogan and Olver [1] and in Mansfield [2]. In particular, we show results for high-dimensional problems and classify those for the three inequivalent SL(2) actions in the plane.

Item Type: | Article |
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Subjects: | Q Science > QA Mathematics (inc Computing science) > QA299 Analysis, Calculus Q Science > QA Mathematics (inc Computing science) > QA372 Ordinary differential equations Q Science > QA Mathematics (inc Computing science) > QA387 Basic Lie theory |

Divisions: | Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science > Applied Mathematics |

Depositing User: | Elizabeth L Mansfield |

Date Deposited: | 09 May 2011 07:28 |

Last Modified: | 15 Jan 2016 15:35 |

Resource URI: | https://kar.kent.ac.uk/id/eprint/27753 (The current URI for this page, for reference purposes) |

ORCiD (Mansfield, Elizabeth L.): | http://orcid.org/0000-0002-6778-2241 |

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