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On the gravity of dumbbell-like bodies represented by a pair of intersecting balls. (Russian. English summary) Zbl 1393.70035
Summary: The problem of the motion of a particle in the gravity field of a homogeneous dumbbell-like body composed of a pair of intersecting balls, whose radii are, in general, different, is studied. Approximation for the Newtonian potential of attraction is obtained. Relative equilibria and their properties are studied under the assumption of uniform rotation of the dumbbells.

MSC:
70K20 Stability for nonlinear problems in mechanics
70K42 Equilibria and periodic trajectories for nonlinear problems in mechanics
70F05 Two-body problems
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[1] [1] Beletsky V. V., Rodnikov A. V., “Coplanar libration points in the generalized restricted circular problem of three bodies”, Nelin. Dinam., 7:3 (2011), 569-576 (Russian)
[2] [2] Karapetyan A. V., Stability of stationary motions, URSS, Moscow, 1998 (Russian)
[3] [3] Kondratyev B. P., Theory of potential. New methods and problems with solutions, Mir, Moscow, 2007 (Russian) · Zbl 0121.23905
[4] [4] Levi-Civita T., Ugo A., Compendio di meccanica razionale: Parte 1. Cinematica — principi e statica, Zanichelli, Bologna, 1946, 423 pp. · Zbl 0020.31502
[5] [5] Beletsky V. V., Rodnikov A. V., “On evolution of libration points similar to Eulerian in the model problem of the binary-asteroids dynamics”, J. Vibroeng., 10:4 (2008), 550-556
[6] [6] Herrera-Succarat E., The full problem of two and three bodies: Application to asteroids and binaries, Univ. of Surrey, Guildford, 2012, 172 pp.
[7] [7] Herrera-Succarat E., Palmer P. L., Roberts M., “Modeling the gravitational potential of a nonspherical asteroid”, J. Guid. Control Dyn., 36:3 (2013), 790-798
[8] [8] Robe H. A. G., “A new kind of \(3\)-body problem”, Celestial Mech., 16:3 (1977), 343-351 · Zbl 0374.70007
[9] [9] Routh E. J., A treatise on stability of a given state of motion, McMillan, London, 1877, 108 pp. · JFM 17.0315.02
[10] [10] Scheeres D., “Relative equilibria in the spherical, finite density \(3\)-body problem”, J. Nonlinear Sci., 26:5 (2016), 1445-1482 · Zbl 1379.70039
[11] [11] Seidov Z. F., Gravitational potential energy of simple bodies: The homogeneous bispherical concavo-convex lens, 2000, 3 pp., arXiv:
[12] [12] Seidov Z. F., Gravitational energy of simple bodies: The method of negative density, 2000, 4 pp., arXiv:
[13] [13] Turconi A., Palmer Ph., Roberts M., “Efficient modelling of small bodies gravitational potential for autonomous proximity operations”, Astrodynamics Network AstroNet-II: The Final Conference, Astrophys. Space Sci. Proc., 44, eds. G. Gómez, J. J. Masdemont, Springer, Cham, 2016, 257-272
[14] [14] Valeriano L. R., “Parametric stability in Robe’s problem”, Regul. Chaotic Dyn., 21:1 (2016), 126-135 · Zbl 1368.70014
[15] [15] Wang X., Jiang Y., Gong S., “Analysis of the potential field and equilibrium points of irregular-shaped minor celestial bodies”, Astrophys. Space Sci., 353:1 (2014), 105-121
[16] [16] Jiang Y., Baoyin H., Li H., “Collision and annihilation of relative equilibrium points around asteroids with a changing parameter”, Mon. Not. R. Astron. Soc., 452:4 (2015), 3924-3931
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