A special case of the problem of three solids

Details A special case of the problem of three solids A special case of the problem of three solids

Oct 1974

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1974azh....51.1079d&link_type=abstract

Astronomicheskii Zhurnal, vol. 51, Sept.-Oct. 1974, p. 1079-1086. In Russian.

Astronomy and Astrophysics

Astronomy

Bodies Of Revolution, Rotating Bodies, Three Body Problem, Translational Motion, Angular Velocity, Classical Mechanics, Convergence, Differential Equations, Ellipsoids, Euler-Lagrange Equation

Scientific paper

The translational-rotational motion of three identical ellipsoids of revolution whose centers are located in a common equatorial plane is analyzed. At the initial moment of time, the ellipsoids form an equilateral triangle. The conditions are determined under which the centers of the ellipsoids will always form an equilateral triangle, moving along similar trajectories about a common center of mass (Lagrangian solution), each ellipsoid rotating about its symmetry axis. If the angular velocity is properly selected, each ellipsoid may be liquid (forming an equilibrium configuration).

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