The Three-Dipole Problem
After investigating the two-dipole problem (first generalization of Stormer–s problem of one magnetic dipole), we proceed one step further along the same lines by setting and investigating the three-dipole problem. Each of the three magnetic dipoles is assumed to be located on one member of a three- star system that performs newtonian motions- Charged particles, positive or negative, moving in the vicinity of the three moving dipoles perform motions which are the object of this study. In this paper we show that if the three stars perform the Lagrangean circular solution of the three-body problem and if the magnetic moments of their dipoles are perpendicular to their plane of motion, then three, or two, or one, closed space inside which charged particles of appropriate energy are permanently trapped. These spaces of trappings can be considered as generalized Van Allen zones.
KeywordsCharged Particle Equilibrium Point Magnetic Dipole Celestial Mechanics Star System
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