Volume 5, Issue 3, August 1998, Pages 289 - 293
A Solvable Many-Body Problem in the Plane
Available Online 1 August 1998.
- https://doi.org/10.2991/jnmp.19220.127.116.11How to use a DOI?
- 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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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.1918.104.22.168 DO - https://doi.org/10.2991/jnmp.1922.214.171.124 ID - CALOGERO1998 ER -