Volume 17, Issue 2, June 2010, Pages 213 - 225
Complex Representation of Planar Motions and Conserved Quantities of the Kepler and Hooke Problems
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/).
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 -