A special case in the problem of three rigid bodies

Details A special case in the problem of three rigid bodies A special case in the problem of three rigid bodies

Oct 1974

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1974sva....18..637d&link_type=abstract

(Astronomicheskii Zhurnal, vol. 51, Sept.-Oct. 1974, p. 1079-1086.) Soviet Astronomy, vol. 18, Mar.-Apr. 1975, p. 637-640. Trans

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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