Hokkaido Mathematical Journal

Moving frames and conservation laws of a Lagrangian invariant under the Hyperbolic Rotation-Translation group

Yousef MASOUDI and Mehdi NADJAFIKHAH

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

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.

Article information

Source
Hokkaido Math. J., Volume 47, Number 3 (2018), 557-579.

Dates
First available in Project Euclid: 26 September 2018

Permanent link to this document
https://projecteuclid.org/euclid.hokmj/1537948831

Digital Object Identifier
doi:10.14492/hokmj/1537948831

Mathematical Reviews number (MathSciNet)
MR3858379

Zentralblatt MATH identifier
06959104

Subjects
Primary: 35L65: Conservation laws 58E30: Variational principles 70S10: Symmetries and conservation laws 53B30: Lorentz metrics, indefinite metrics 53C50: Lorentz manifolds, manifolds with indefinite metrics 58D19: Group actions and symmetry properties 43A65: Representations of groups, semigroups, etc. [See also 22A10, 22A20, 22Dxx, 22E45]

Keywords
Conservation laws Moving frames Differential invariants Normalized differential invariants Syzygies Killing vector fields

Citation

MASOUDI, Yousef; NADJAFIKHAH, Mehdi. Moving frames and conservation laws of a Lagrangian invariant under the Hyperbolic Rotation-Translation group. Hokkaido Math. J. 47 (2018), no. 3, 557--579. doi:10.14492/hokmj/1537948831. https://projecteuclid.org/euclid.hokmj/1537948831


Export citation