Classification of a class of relative equilibria in three body coulomb systems

We consider a class of relative equilibria of a non-regularized ensemble of three charged particles in the fully three-dimensional Euclidean space, i.e., uniform rotational motions of (i) one negative and one positive point charge as well as the “classical” case of (ii) two negative point charges in the electrostatic field of a fixed positive point charge, such that the mutual distances between the three particles and the axis of rotation stay constant over time. Depending on the physical parameters this kind of relative equilibria of such systems are completely classified. Thereby, all our considerations deal with arbitrary positive and negative charge values of the particles as well as arbitrary values for the masses of the freely movable ones.