Stationary motions in the threespheroidalbody problem
Abstract
It is shown that the three body problem of homogeneous ellipsoids of revolution has triangular and rectangular solutions of Euler and Lagrange type. For rectangular solutions, the axes of symmetry of the bodies can be directed along the centerlines as well as in the plane of the orthogonal centerline. For triangular solutions, if the masses of two of the bodies are equal, the axis of symmetry of the third body can lie in the plane of the triangle. The problem can also have a solution which does not exist in the classical three body problem, namely, the case where the centers of mass of two of the ellipsoids move in one plane, while the center of mass of the third ellipsoid moves in a plane parallel to the first plane.
 Publication:

Moskovskii Universitet Vestnik Seriia Matematika Mekhanika
 Pub Date:
 1977
 Bibcode:
 1977MVSMM..32...95M
 Keywords:

 Bodies Of Revolution;
 Celestial Mechanics;
 Ellipsoids;
 EulerLagrange Equation;
 Three Body Problem;
 Angular Velocity;
 Equations Of Motion;
 Partial Differential Equations;
 Astronomy