The regular polygon problem of (N+2) bodies: a numerical investigation of the equilibrium states of the minor bodies
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In this paper we study some aspects of the dynamics of a pair of weakly interacting small bodies which also undergo the influence of N big bodies, ν=N−1 of which have equal masses and are arranged at the vertices of a regular polygon formation, while the Nth body has a different mass and is located at the centre of mass of this formation. By assuming that the big bodies are in relative equilibrium and that the whole formation rotates about a vertical axis with constant angular velocity, we formulate the problem by giving the equations which describe the motion of the two minor bodies in a synodic coordinate system attached to the big bodies and we numerically investigate their equilibrium locations, their parametric variation and their state of stability.
KeywordsDynamics of a dual satellites’ system in a regular polygon configuration of N bodies Equilibrium locations Parametric variation Stability
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