Abstract:
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.
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