On a restricted (2n+3)body problem
Abstract
We consider the case of (2n+1) bodies (n≥0) each of mass m, which are placed on a circle with radius r, such that they form a regular polygon: an equilateral (2n+1)angle. In the centre of the circle a body of mass b times m is placed, where b is chosen large enough to ensure stability of the system; only gravitational interaction is considered. Each of the bodies rotates uniformly around the centre with angular velocity ω. In addition to the (2n+2) bodies, considered to be point masses, we have another point mass with negligible mass compared to the former ones; we are then interested in the motion of the small body in the gravitational field of force generated by the large ones, moving themselves in an equilibrium configuration reacting to each other's fields of force but not to the (2n+3)d body.
 Publication:

Celestial Mechanics
 Pub Date:
 March 1988
 DOI:
 10.1007/BF01228997
 Bibcode:
 1988CeMec..45..163O