A~new goldfish model
Teoretičeskaâ i matematičeskaâ fizika, Tome 167 (2011) no. 3, pp. 364-376
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A new integrable (indeed, solvable) model of goldfish type is
identified, and some of its properties are discussed. A version of its
Newtonian equations of motion reads as follows:
$$
\ddot{z}_n=\frac{\beta\dot{z}_n(\dot{z}_n+\eta)}{1+\beta z_n}+
\sum_{m=1,m\ne n}^N\frac{(\dot{z}_n-\beta\eta z_n)
(\dot{z}_m-\beta\eta z_m)\bigl[2+\beta(z_n+z_m)\bigr]}
{(z_n-z_m)(1+\beta z_m)},
$$
where $z_n\equiv z_n(t)$ are the $N$ dependent variables, $t$ is the independent variable (“time”), the dots indicate time
differentiations, and $\beta$, $\eta$ are two arbitrary constants.
Keywords:
integrable dynamical system, solvable dynamical system, integrable Newtonian many-body problem.
@article{TMF_2011_167_3_a3,
author = {F. Calogero},
title = {A~new goldfish model},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {364--376},
publisher = {mathdoc},
volume = {167},
number = {3},
year = {2011},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2011_167_3_a3/}
}
F. Calogero. A~new goldfish model. Teoretičeskaâ i matematičeskaâ fizika, Tome 167 (2011) no. 3, pp. 364-376. http://geodesic.mathdoc.fr/item/TMF_2011_167_3_a3/