On the Lagrangian problem of three fixed centers.
Abstract
The problem of the motion of a body subjected to the gravitational attraction of two fixed centers and a Hookean force directed toward the midpoint between the two fixed centers is investigated. Possible applications of this problem in studies of galactic dynamics are noted. The relevant equations of motion are integrated, and two hyperelliptic equations are obtained whose form is simplified by parameter substitution. The relation between this problem and the circular restricted threebody problem is briefly discussed.
 Publication:

Dynamics of the Galaxy and Extragalactic Systems
 Pub Date:
 1976
 Bibcode:
 1976dges.book...29I
 Keywords:

 Celestial Mechanics;
 Galactic Rotation;
 Lagrangian Equilibrium Points;
 Three Body Problem;
 Astrodynamics;
 Elliptic Functions;
 Hookes Law;
 Astronomy