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Nonlinear analysis of the stability of the libration points of a triaxial ellipsoid. (English. Russian original) Zbl 0591.70026
J. Appl. Math. Mech. 49, 10-16 (1985); translation from Prikl. Mat. Mekh. 49, 16-24 (1985).
Summary: The stability of libration points of a triaxial homogeneous gravitating ellipsoid rotating around one of its principal central axes of inertia is studied. The plane motion of a passive point of unit mass is considered. In parameter space a region of stability is constructed and, also, resonance sets for all the resonances investigated. A systematic analysis of the stability of a libration point is carried out, using respective theorems for the equilibrium positions of Hamiltonian systems with two degrees of freedom.

MSC:
70K30 Nonlinear resonances for nonlinear problems in mechanics
70K20 Stability for nonlinear problems in mechanics
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