Geodesic
Another new goldfish model
Teoretičeskaâ i matematičeskaâ fizika, Tome 171 (2012) no. 2, pp. 241-253 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. Its Newtonian equations of motion read as follows: \begin{align*} \ddot z_n={}&\frac{\dot z_n^2}{z_n}+c_1\frac{\dot z_n}{z_n}+ c_2\dot z_n+c_2c_3z_n+c_1c_2+{} \\[2mm] &{}+\sum_{m=1,m\ne n}^N\frac{(\dot z_n+c_3z_n+c_1)(\dot z_m+c_3z_m+c_1)} {z_m}\cdot\frac{z_n+z_m}{z_n-z_m},\quad n=1,\dots,N, \end{align*} where $c_1$, $c_2$, and $c_3$ are arbitrary constants, $z_n\equiv z_n(t)$ are the $N$ dependent variables, $N$ is an arbitrary positive number $(N>1)$, $t$ is the independent variable {(}“time”{\rm)} and the dots indicate time-differentiations.
Keywords: integrable dynamical systems, solvable dynamical systems, integrable Newtonian many-body problems. 
@article{TMF_2012_171_2_a4,
     author = {F. Calogero},
     title = {Another new goldfish model},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {241--253},
     year = {2012},
     volume = {171},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2012_171_2_a4/}
}
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F. Calogero. Another new goldfish model. Teoretičeskaâ i matematičeskaâ fizika, Tome 171 (2012) no. 2, pp. 241-253. http://geodesic.mathdoc.fr/item/TMF_2012_171_2_a4/

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