Journal of Nonlinear Mathematical Physics

<Previous Article In Issue
Next Article In Issue>
Volume 19, Issue 1, March 2012, Pages 62 - 80

New Solvable Many-Body Model of Goldfish Type

Authors
F. Calogero
Physics Department, University of Rome “La Sapienza”, Istituto Nazionale di Fisica Nucleare, Sezione di Roma, Italy,francesco.calogero@roma1.infn.it,francesco.calogero@uniroma1.it
Received 4 September 2011, Accepted 7 November 2011, Available Online 6 January 2021.
DOI
10.1142/S1402925112500064How to use a DOI?
Keywords
Integrable dynamical systems; solvable dynamical systems; integrable Newtonian many-body problems; solvable Newtonian many-body problems; isochronous dynamical systems
Abstract

A new solvable N-body model of goldfish type is identified. Its Newtonian equations of motion read as follows:

z&die;n=-6z&dot;nzn-4zn3+32(z&dot;n+2zn2)∑k=1N(z&dot; kzk+2zk)+2∑&lscr;=1,&lscr;≠nN[(z&dot;n+2zn2)(z&dot;&lscr;+2z&lscr;2)zn-z&lscr;],      n=1,…,N,
where zn ≡ zn(t) are the N dependent variables (with N an arbitrary positive integer), t is the independent variable (“time”) and the dots indicate time-differentiations. Its isochronous variant is also obtained and discussed. Other new solvable models of goldfish type characterize the behavior of these systems in the immediate neighborhood of their equilibria.

Copyright
© 2012 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/).

Download article (PDF)

<Previous Article In Issue
Next Article In Issue>
Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
19 - 1
Pages
62 - 80
Publication Date
2021/01/06
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.1142/S1402925112500064How to use a DOI?
Copyright
© 2012 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

risenwbib
TY  - JOUR
AU  - F. Calogero
PY  - 2021
DA  - 2021/01/06
TI  - New Solvable Many-Body Model of Goldfish Type
JO  - Journal of Nonlinear Mathematical Physics
SP  - 62
EP  - 80
VL  - 19
IS  - 1
SN  - 1776-0852
UR  - https://doi.org/10.1142/S1402925112500064
DO  - 10.1142/S1402925112500064
ID  - Calogero2021
ER  -