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 |

##### Keywords:

rotation around principal central axes of inertia; third-order; resonance; stability of libration points; triaxial homogeneous gravitating ellipsoid; plane motion of a passive point of unit mass; region of stability; resonance sets; equilibrium positions of Hamiltonian systems
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\textit{I. I. Kosenko}, J. Appl. Math. Mech. 49, 10--16 (1985; Zbl 0591.70026); translation from Prikl. Mat. Mekh. 49, 16--24 (1985)

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##### References:

[1] | Smale, S., Topology and mechanics, Invent. math., Vol.10, No.4, (1970) · Zbl 0202.23201 |

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[3] | Tatarinov, Ya.V., The geometric formalism of classical dynamics, () · Zbl 0525.70022 |

[4] | Sharlier, K., Celestial mechanics, (1967), Nauka Moscow |

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