Atlantis Press Paper Details: A Solvable Many-Body Problem in the Plane

A solvable many-body problem in the plane is exhibited. It is characterized by rotation-invariant Newtonian ("acceleration equal force") equations of motion, featuring one-body ("external") and pair ("interparticle") forces. The former depend quadratically on the velocity, and nonlinearly on the coordinate, of the moving particle. The latter depend linearly on the coordinate of the moving particle, and linearly respectively nonlinearly on the velocity respectively the coordinate of the other particle. The model contains 2n2 arbitrary coupling constants, n being the number of particles. The behaviour of the solutions is outlined; special cases in which the motion is confined (multiply periodic), or even completely periodic, are identified.

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title:		A Solvable Many-Body Problem in the Plane
publication:		JNMP
volume-issue:		5 - 3
pages:		289 - 293
ISSN:		1402-9251
DOI:		doi:10.2991/jnmp.1998.5.3.4 (how to use a DOI)
author(s):		F. CALOGERO
publication date:		August 1998
abstract:		A solvable many-body problem in the plane is exhibited. It is characterized by rotation-invariant Newtonian ("acceleration equal force") equations of motion, featuring one-body ("external") and pair ("interparticle") forces. The former depend quadratically on the velocity, and nonlinearly on the coordinate, of the moving particle. The latter depend linearly on the coordinate of the moving particle, and linearly respectively nonlinearly on the velocity respectively the coordinate of the other particle. The model contains 2n2 arbitrary coupling constants, n being the number of particles. The behaviour of the solutions is outlined; special cases in which the motion is confined (multiply periodic), or even completely periodic, are identified.
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:		53art2.pdf (92 K)