Various many-body models are treated, which describe $N$ points confined to move on a plane circle. Their Newtonian equations of motion (“accelerations equal forces”) are integrable, i.e., they allow the explicit exhibition of $N$ constants of motion in terms of the dependent variables and their time-derivatives. Some of these models are moreover solvable by purely algebraic operations, by (explicitly performable) quadratures and, finally, by functional inversions. The techniques to manufacture these models are not new; some of these models are themselves new; others are reinterpretations of known models.
Oksana Bihun. Francesco Calogero. "Solvable and/or Integrable Many-Body Models on a Circle." J. Geom. Symmetry Phys. 30 1 - 18, 2013. https://doi.org/10.7546/jgsp-30-2013-1-18