On the restricted circular three-charged-body problem |
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Authors: | D D Dionysiou D A Vaiopoulos |
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Institution: | 1. Department of Mathematics, Hellenic Air-Force Academy, Dekelia, Attica, Greece 2. Department of Geology, University of Athens, Panepistimiopolis, Athens, Greece
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Abstract: | Two-charged bodiesM 1 andM 2 revolve round their centre of mass in circular orbits under Newton's inverse-square law and the so similar Coulomb's law. A third-charged-bodyM, without mass and charge (i.e., such that it is attracted or repulsed byM 1 andM 2, but does not influence their motion), moves in a field with a force function, namely $$U = {\text{ }}\frac{{q - \mu }}{{r_1 }}{\text{ }} + {\text{ }}\frac{{\mu - q}}{{r_2 }}$$ , which is created byM 1 andM 2. In what follows, the existence and location of the collinear and equilateral Lagrangian points or solutions with be discussed and the interpretation of them will be given. This work is a generalization of the classical restricted circular three-body problem. |
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