Journal of Nonlinear Mathematical Physics

Volume 5, Issue 3, August 1998, Pages 289 - 293

A Solvable Many-Body Problem in the Plane

Authors
F. CALOGERO
Corresponding Author
F. CALOGERO
Available Online 1 August 1998.
DOI
https://doi.org/10.2991/jnmp.1998.5.3.4How to use a DOI?
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.
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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
5 - 3
Pages
289 - 293
Publication Date
1998/08
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.2991/jnmp.1998.5.3.4How to use a DOI?
Open Access
This is an open access article distributed under the CC BY-NC license.

Cite this article

TY  - JOUR
AU  - F. CALOGERO
PY  - 1998
DA  - 1998/08
TI  - A Solvable Many-Body Problem in the Plane
JO  - Journal of Nonlinear Mathematical Physics
SP  - 289
EP  - 293
VL  - 5
IS  - 3
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.1998.5.3.4
DO  - https://doi.org/10.2991/jnmp.1998.5.3.4
ID  - CALOGERO1998
ER  -