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

Pages: 1254 - 1262, Issue Special, September 2011

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Florian Rupp - Lehrstuhl für Höhere Mathematik und Analytische Mechanik, Technische Universität München, Fakultät für Mathematik, D-85747 Garching, Germany (email)
Jürgen Scheurle - Technische Universität München, Zentrum Mathematik, Boltzmannstraße 3, D-85748 Garching, Germany (email)

Abstract: 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.

Keywords:  Coulomb three body problem, Relative equilibira
Mathematics Subject Classification:  Primary: 37J25, 37J15, 70F07, 70H12, 70H14; Secondary: 58Z05

Received: August 2010;      Revised: September 2010;      Published: October 2011.