Journal of Nonlinear Mathematical Physics

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/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
12 - 2
Pages
253 - 267
Publication Date
2005/05/01
ISBN
91-974824-4-7
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.2991/jnmp.2005.12.2.7How to use a DOI?
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  -