Triangular dynamics under pressure

Three planar classical particles interact via a potential proportional to the area of the triangle they form. This system is equivalent to two oscillators attached to the origin, the nearest being repelled by and the other being attracted to it (piecewise integrable Hamiltonian). Numerical simulations show two types of trajectories: those apparently escaping to infinity, and those in confined quasiperiodic orbits. Adiabatic theories lead to discrete recurrence relations and allow for the second type only. A general method allowing prediction of first return time of the slow motion as well as a short/long-period relation is presented. The issue of the possibly metastable nature of escaping trajectories is raised.Dedicated to Prof. Philippe Choquard.