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Stability of motion of the restricted circular and charged three-body problem
Authors:D D Dionysiou  G G Stamou
Institution:1. Department of Mathematics, Hellenic Air-Force Academy, Dekelia, Attica, Greece
Abstract:Stabiliity is applied to characterize type of motion in which the moving body is confined to certain limited regions and in this sense we may say that the motion of the body in question is stable. This method has been used in the past chiefly in connection with the classical restricted problem of three bodies.In this paper we consider a dynamical system defined by the Lagrangian

$$L = \tfrac{1}{2}(\dot x^2  + \dot y^2  + \dot z^2 ) + x\dot y - y\dot x + \tfrac{1}{2}(x^2  + y^2 ) + \frac{{q - \mu }}{{r_1 }} + \frac{{\mu  - q}}{{r_2 }}$$
Keywords:
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