Journal of Nonlinear Mathematical Physics

Volume 17, Issue 2, June 2010, Pages 213 - 225

Complex Representation of Planar Motions and Conserved Quantities of the Kepler and Hooke Problems

Authors
Y. Grandati*, A. Bérard, H. Mohrbach
Institut de Physique, ICPMB, IF CNRS 2843, Université Paul Verlaine, 1 Bvd Arago, 57078 Metz, Cedex 3, France
Received 29 September 2009, Accepted 15 November 2009, Available Online 7 January 2021.
DOI
10.1142/S1402925110000726How to use a DOI?
Keywords
Planar motions; Bohlin–Arnold–Vassiliev duality; complex representation; conserved quantities
Abstract

Using a complex representation of planar motions, we show that the dynamical conserved quantities associated to the isotropic harmonic oscillator (Fradkin–Jauch–Hill tensor) and to the Kepler's problem (Laplace–Runge–Lenz vector) find a very simple and natural interpretation. In this frame we also establish in an elementary way the relation which connects them.

Copyright
© 2010 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
17 - 2
Pages
213 - 225
Publication Date
2021/01/07
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.1142/S1402925110000726How to use a DOI?
Copyright
© 2010 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - JOUR
AU  - Y. Grandati
AU  - A. Bérard
AU  - H. Mohrbach
PY  - 2021
DA  - 2021/01/07
TI  - Complex Representation of Planar Motions and Conserved Quantities of the Kepler and Hooke Problems
JO  - Journal of Nonlinear Mathematical Physics
SP  - 213
EP  - 225
VL  - 17
IS  - 2
SN  - 1776-0852
UR  - https://doi.org/10.1142/S1402925110000726
DO  - 10.1142/S1402925110000726
ID  - Grandati2021
ER  -