A Solvable N-body Problem of Goldfish Type Featuring N2 Arbitrary Coupling Constants
- DOI
- 10.1080/14029251.2016.1175823How to use a DOI?
- Keywords
- Solvable N-body problems; integrable N-body problems; integrable dynamical systems
- Abstract
A N-body problem “of goldfish type” is introduced, the Newtonian (“acceleration equal force”) equations of motion of which describe the motion of N pointlike unit-mass particles moving in the complex z-plane. The model—for arbitrary N—is solvable, namely its configuration (positions and velocities of the N “particles”) at any later time t can be obtained from its configuration at the initial time by algebraic operations. It features specific nonlinear velocity-dependent many-body forces depending on N2 arbitrary (complex) coupling constants. Sufficient conditions on these constants are identified which cause the model to be isochronous—so that all its solutions are then periodic with a fixed period independent of the initial data. A variant with twice as many arbitrary coupling constants, or even more, is also identified.
- Copyright
- © 2016 The Authors. Published by Atlantis Press and Taylor & Francis
- Open Access
- This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - JOUR AU - Francesco Calogero PY - 2021 DA - 2021/01/06 TI - A Solvable N-body Problem of Goldfish Type Featuring N² Arbitrary Coupling Constants JO - Journal of Nonlinear Mathematical Physics SP - 300 EP - 305 VL - 23 IS - 2 SN - 1776-0852 UR - https://doi.org/10.1080/14029251.2016.1175823 DO - 10.1080/14029251.2016.1175823 ID - Calogero2021 ER -