Solvable and/or Integrable Many-Body Models on a Circle

Abstract

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.