Volume 12, Issue 2, May 2005, Pages 253 - 267
Triangular Newton Equations with Maximal Number of Integrals of Motion
Authors
Fredrik Persson, Stefan Rauch-Wojciechowski
Corresponding Author
Fredrik Persson
Received 1 January 2005, Accepted 1 January 2005, Available Online 1 May 2005.
- DOI
- 10.2991/jnmp.2005.12.2.7How to use a DOI?
- Abstract
We study two-dimensional triangular systems of Newton equations (acceleration = velocity-independent force) admitting three functionally independent quadratic intgrals of motion. The main idea is to exploit the fact that the first component M1(q1) of a triangular force depends on one variable only. By using the existence of extra integrals of motion we reduce the problem to solving a simultaneous system of three linear ordinary differential equations with nonconstant coefficients for M1(q1). With the help of computer algebra we have found and solved these ordinary differential equations in all cases. A complete list of superintegrable triangular equations in two dimensions is been given. Most of these equations were not known before.
- Copyright
- © 2006, the Authors. Published by Atlantis Press.
- Open Access
- This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - JOUR AU - Fredrik Persson AU - Stefan Rauch-Wojciechowski PY - 2005 DA - 2005/05/01 TI - Triangular Newton Equations with Maximal Number of Integrals of Motion JO - Journal of Nonlinear Mathematical Physics SP - 253 EP - 267 VL - 12 IS - 2 SN - 1776-0852 UR - https://doi.org/10.2991/jnmp.2005.12.2.7 DO - 10.2991/jnmp.2005.12.2.7 ID - Persson2005 ER -