General solution of a three-body problem in the plane

We provide and discuss the general solution of a (Hamiltonian) three-body problem in the plane, characterized by Newtonian equations of motion with rotation- and translation-invariant velocity-dependent one-body and two-body forces. The model features a (nonnegative) real parameter omega: when it does not vanish, all solutions are completely periodic with period T = 2pi/omega; when it vanishes, both unbounded and confined motions are possible with a rather rich phenomenology of possible behaviour in the latter case, including completely periodic motions and limit cycles.