zbMATH — the first resource for mathematics

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.

70K30 Nonlinear resonances for nonlinear problems in mechanics
70K20 Stability for nonlinear problems in mechanics
Full Text: DOI
[1] Smale, S., Topology and mechanics, Invent. math., Vol.10, No.4, (1970) · Zbl 0202.23201
[2] Groyachev, D.N., Some general integrals in the problem of the motion of a solid, (1910), Warsaw
[3] Tatarinov, Ya.V., The geometric formalism of classical dynamics, () · Zbl 0525.70022
[4] Sharlier, K., Celestial mechanics, (1967), Nauka Moscow
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.