A Solvable Many-Body Problem in the Plane

DOI

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.

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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TY  - JOUR
AU  - F. Calogero
PY  - 1998
DA  - 1998/08/01
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  - 10.2991/jnmp.1998.5.3.4
ID  - Calogero1998
ER  -