The asymptotic stability of the relative equilibria of point masses in a weakly resistive medium in the gravitational field of a rotating ellipsoid.

*(English. Russian original)*Zbl 1423.70037
J. Appl. Math. Mech. 76, No. 4, 435-440 (2012); translation from Prikl. Mat. Mekh. 76, No. 4, 601-609 (2012).

Summary: The motion of a point mass in the gravitational field of a rotating triaxial ellipsoid that is homogeneous or inhomogeneous but with ellipsoidal layers of equal density is considered. In addition to the gravitational and centrifugal forces, the force of the weakly resistive medium acts on the point mass. It is shown that the libration points in this extended problem turn out to be displaced with respect to the position of the libration points of the classical problem by small amounts in the direction of rotation of the ellipsoid. Moreover, it is proved that, if dissipative forces (resistances) act on the motion of the point mass in an absolute system of coordinates, the displaced points, which are stable in the first approximation, become asymptotically stable.

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\textit{S. F. Zhuravlëv}, J. Appl. Math. Mech. 76, No. 4, 435--440 (2012; Zbl 1423.70037); translation from Prikl. Mat. Mekh. 76, No. 4, 601--609 (2012)

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##### References:

[1] | Thomson, W.; Tait, P., Treatise on natural philosophy pt. I, (1879), Univ. Press Cambridge · JFM 15.0767.01 |

[2] | Chetayev, N.G., The stability of motion. papers in analytical mechanics, (1962), Izd Akad Nauk SSSR Moscow |

[3] | Rumyantsev, V.V., Two problems on the stability of motion, Izv akad nauk SSSR MTT, 5, 5-12, (1975) |

[4] | Ivanov, A.P., The effect of small resistance forces on relative equilibrium, Prikl mat mekh, 58, 5, 22-30, (1994) |

[5] | Ivanov, A.P.; Sokolovskaya, V.V., The stability of the triangular libration points of the three-body problem in a resistive medium, Kosm issled, 35, 5, 495-500, (1997) |

[6] | Agrest, M.M., On the stability of the librational solutions in the bounded circular three-body problem in a resistive medium, Tr GoS astron inst im P K sternberg, 15, 1, 363-379, (1945) |

[7] | Zhuravlev, S.G., Stability of the libration points of a rotating triaxial ellipsoid, Celest mech, 6, 3, 255-267, (1972) · Zbl 0254.70007 |

[8] | Clarke, A.C., Extra-terrestrial relays. can rockets stations give world-wide radio coverage?, Wireless world, 51, 305-308, (1945), Okt |

[9] | Batrakov, YuV., Periodic motions of a particle in the gravitational field of a rotating triaxial ellipsoid, Byull inst teor astron akad nauk SSSR, 6, 8, 524-542, (1957) |

[10] | Abalakin, V.K., On the question of the stability of libration points in the neighbourhood of a rotating gravitating ellipsoid, Byull inst teor astron akad nauk SSSR, 6, 8, 543-549, (1957) |

[11] | Zhuravlev, S.G., About stability of the libration points of a rotating triaxial ellipsoid in a degenerate case, Celest mech, 8, 1, 75-84, (1973) · Zbl 0276.70011 |

[12] | Zhuravlev, S.G., On the stability of the libration points of a rotating triaxial ellipsoid in the three-dimensional case, Astron zh, 51, 6, 1330-1334, (1974) · Zbl 0288.70007 |

[13] | Kosenko, I.I., On libration points near a gravitating and rotating triaxial ellipsoid, J appl math mech, 45, 1, 18-23, (1981) · Zbl 0486.70013 |

[14] | Kosenko, I.I., Libration points in the problem of a triaxial gravitating ellipsoid, Geometry of the stability domain kosm issled, 19, 2, 200-209, (1981) · Zbl 0486.70013 |

[15] | Markeyev, A.P., Libration points in celestial mechanics and space dynamics, (1978), Nauka Moscow |

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