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October 2018 Moving frames and conservation laws of a Lagrangian invariant under the Hyperbolic Rotation-Translation group
Yousef MASOUDI, Mehdi NADJAFIKHAH
Hokkaido Math. J. 47(3): 557-579 (October 2018). DOI: 10.14492/hokmj/1537948831

Abstract

Noether's First Theorem guarantees conservation laws provided that the Lagrangian is invariant under a Lie group action. In this paper, via the concept of Killing vector fields and the Minkowski metric, we first construct an important Lie group, known as Hyperbolic Rotation-Translation group. Then, according to Gonçalves and Mansfield's method, we obtain the invariantized Euler-Lagrange equations and the space of conservation laws in terms of vectors of invariants and the adjoint representation of a moving frame, for Lagrangians, which are invariant under Hyperbolic Rotation-Translation (or HRT) group action, in the case where the independent variables are not invariant.

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Yousef MASOUDI. Mehdi NADJAFIKHAH. "Moving frames and conservation laws of a Lagrangian invariant under the Hyperbolic Rotation-Translation group." Hokkaido Math. J. 47 (3) 557 - 579, October 2018. https://doi.org/10.14492/hokmj/1537948831

Information

Published: October 2018
First available in Project Euclid: 26 September 2018

zbMATH: 06959104
MathSciNet: MR3858379
Digital Object Identifier: 10.14492/hokmj/1537948831

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Rights: Copyright © 2018 Hokkaido University, Department of Mathematics

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Vol.47 • No. 3 • October 2018
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