Atlantis Press Paper Details: Triangular Newton Equations with Maximal Number of Integrals of Motion

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.

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title:		Triangular Newton Equations with Maximal Number of Integrals of Motion
publication:		JNMP
volume-issue:		12 - 2
pages:		253 - 267
ISSN:		1402-9251
DOI:		doi:10.2991/jnmp.2005.12.2.7 (how to use a DOI)
author(s):		Fredrik PERSSON, Stefan RAUCH-WOJCIECHOWSKI
publication date:		May 2005
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:		© Atlantis Press. This article is distributed under the terms of the Creative Commons Attribution License, which permits non-commercial use, distribution and reproduction in any medium, provided the original work is properly cited.
full text:		122art7.pdf (168 K)