Geodesic
A new goldfish model
Teoretičeskaâ i matematičeskaâ fizika, Tome 167 (2011) no. 3, pp. 364-376 Cet article a éte moissonné depuis la source Math-Net.Ru

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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},
     year = {2011},
     volume = {167},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2011_167_3_a3/}
}
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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/

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