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

Alexander V. Rodnikov

Russian journal of nonlinear dynamics, Tome 10 (2014) no. 2, pp. 213-222.

Résumé

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.

Détail

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

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