Physics
Scientific paper
Nov 1974
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1974cemec..10..327k&link_type=abstract
Celestial Mechanics, vol. 10, Nov. 1974, p. 327-344.
Physics
3
Celestial Mechanics, Euler-Lagrange Equation, Lagrangian Equilibrium Points, Orbital Elements, Three Body Problem, Earth-Moon System, Gravitational Effects, Rotating Bodies, Satellite Orbits
Scientific paper
The present paper is a direct continuation of a paper (Duboshin, 1973) in which the existence of one kind of Lagrange (triangular) and Euler (rectilinear) solutions of the general problem of the motion of three finite rigid bodies was proven, assuming different laws of interaction between the elementary particles of the rigid bodies. In particular, Duboshin found that the general problem of three rigid bodies permits solutions in which the centers of mass of the bodies always form an equilateral triangle or always remain on one straight line, and each body possesses an axial symmetry and a symmetry with respect to the plane of the centers of mass and rotates uniformly about its axis orthogonal to this plane. In the present paper new Lagrange solutions of the above-mentioned general problems of three rigid bodies of 'level' type are found when the axes of geometrical and mechanical symmetry of all three bodies always lie in the triangle plane, and the bodies themselves rotate inertially around the symmetry axis, independently of the parameters of the orbital motion of the centers of mass.
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