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 Nelin. Dinam., 2014, Volume 10, Number 2, Pages 213–222 (Mi nd438)

Triangular libration points of the generalized restricted circular problem of three bodies for conjugate complex masses of attracting centers

Alexander V. Rodnikov

Bauman Moscow State Technical University, 2nd Baumanskaya st. 5, Moscow, 105005, Russia

Abstract: We study a particle equilibria with respect to axes of precession and of dynamical symmetry of a rigid body in assumption that the body gravitational field is composed of gravitational fields of two conjugate complex masses being on imaginary distance. We establish that there are not more then two of these equilibria in the plane passing the body mass center orthogonally to the precession axis. Using terminology of the Generalized Restricted Circular Problem of Three Bodies, we call these equilibria the Triangular Libration Points (TLP). We find TLPs' coordinates analytically and we trace their evolution at changing values of the system parameters. We also prove that TLPs are instable.

Keywords: problem of three bodies, libration points, relative equilibrium, rigid body, asteroid.

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UDC: 531.36:521.1
MSC: 70K20, 70K42
Revised: 13.03.2014

Citation: Alexander V. Rodnikov, “Triangular libration points of the generalized restricted circular problem of three bodies for conjugate complex masses of attracting centers”, Nelin. Dinam., 10:2 (2014), 213–222

Citation in format AMSBIB
\Bibitem{Rod14} \by Alexander~V.~Rodnikov \paper Triangular libration points of the generalized restricted circular problem of three bodies for conjugate complex masses of attracting centers \jour Nelin. Dinam. \yr 2014 \vol 10 \issue 2 \pages 213--222 \mathnet{http://mi.mathnet.ru/nd438} 

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This publication is cited in the following articles:
1. A. V. Rodnikov, “Modelirovanie dinamiki kosmicheskoi stantsii v okrestnosti asteroida”, Mat. modelir. i chisl. metody, 2016, no. 10, 55–68
2. A. A. Burov, A. D. German, E. A. Raspopova, V. I. Nikonov, “O primenenii $K$-srednikh dlya opredeleniya raspredeleniya mass ganteleobraznykh nebesnykh tel”, Nelineinaya dinam., 14:1 (2018), 45–52
3. A. V. Rodnikov, “On safe configurations of a natural-artificial space tether system”, Eighth Polyakhov's Reading, AIP Conf. Proc., 1959, eds. E. Kustova, G. Leonov, N. Morosov, M. Yushkov, M. Mekhonoshina, Amer. Inst. Phys., 2018, UNSP 040018
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