Article:
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F. Rupp & J. Scheurle (2011): Classification of a Class of Relative
Equilibria in Three Body Coulomb Systems, Dynamical Systems and
Differential Equations, DCDS Supplement 2011 Proceedings of the
8th AIMS International Conference (Dresden, Germany), pp. 1254-1262.
Abstract:
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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.