Stationary motions in the problem of three ellipsoids of revolution

Details Stationary motions in the problem of three ellipsoids of revolution Stationary motions in the problem of three ellipsoids of revolution

Feb 1977

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1977mvsmm.......95m&link_type=abstract

Moskovskii Universitet, Vestnik, Seriia I - Matematika, Mekhanika, Jan.-Feb. 1977, p. 95-101. In Russian.

Physics

Bodies Of Revolution, Celestial Mechanics, Ellipsoids, Euler-Lagrange Equation, Three Body Problem, Angular Velocity, Equations Of Motion, Partial Differential Equations

Scientific paper

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.

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