and Computational Methods

doi: 10.18698/2309-3684-2016-2-5568

We suggest classification for dynamical problems of a space station motion near a precessing small planet. This classification is based on three signs. These signs are the model of the asteroid gravitational potential, the method of holding the space station near the small planet, the type of dynamical problem. Within the offered classification we review the results received earlier. In particular, we construct sets of the space station equilibria or stationary orbits if the asteroid gravitational potential is composed by potentials of two real or conjugate complex point masses on real or imaginary distance and if the station coast along the leier or it moves freely. (In our case the leier is a tether with ends fixed in the asteroid poles). Moreover, we establish some facts of stability for the found orbits and equilibria and note some integrable cases of the motion equations along the leier

[1] Ivashkin, V.V., Stikhno, C.A. On the problem of orbit correction for the near-Earth (99942) asteroid Apophis. Doklady Physics, 2008, т. 419, № 5.

[2] Ivashkin, V.V., Stikhno, C.A. On the use of the gravitational effect for orbit correction of the asteroid apophis. Doklady Physics, 2009, т. 424, № 5. С. 621-626.

[3] Ivashkin, V.V., Stikhno, C.A. On the prevention of a possible collision of asteroid Apophis with the Earth. Solar System Research, 2009, т. 43, № 6, с. 483-496.

[4] Beletsky V.V. Generalized Restricted Circular Three-Body Problem as a Model for Dynamics of Binary Asteroids. Cosmic Research. 2007, v. 45, 5, p. 408-416.

[5] Beletsky V.V., Rodnikov A.V. Stability of Triangle Libration Points in Generalized Restricted Circular Three-Body Problem. Cosmic Research, 2008, v. 46, 1, p. 40-48.

[6] 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., 2008, vol. 10, no. 4, p. 550–556

[7] Beletsky V.V., Rodnikov A.V. Coplanar Libration Points in the Generalized Restricted Circular Problem of Three Bodies. Rus. J. Nonlin. Dyn., 2011, vol. 7, no. 3, pp. 569–576.

[8] Zimin V.N., Krylov A.V., Meshkovskii V.E., Sdobnikov A.N., Faizullin F.R., Churilin S.A. Features of the Calculation Deployment Large Transformable Structures of Different Configurations. Science & Education, scientific edition of BMSTU, 2014, № 10. с. 179-191

[9] Zimin V.N., Krylov A.V., Churilin S.A. Modelirovanie dinamiki raskrytiya krupnogabaritnykh transformiruemykh konstruktsii. In: The XIth all-russian congress on basic problems of theoretical and applied mechanics, collection of papers, 2015, Kazan’, p. 1499-1501.

[10] Rodnikov A.V. The Algorithm for Capture of the Space Garbage Using “Leier Constraint”. Regular and Chaotic Dynamics, 2006, v.11, 4, pp. 483-489

[11] Bazey A., Bazey N., Borovin G., Zolotov V., Kashuba V., Kashuba S., Kupriyanov V., Molotov I. Evolution of the orbit of a passive fragment with a large area of surface in high Earth orbit. Mathematical Modeling and Computational Methods, 2015, №1 (5), pp. 83-93

[12] Bushuev A., Farafanov B. Mathematical modelling of deployment of large-area solar array. Маthematical Modeling and Computational Methods, 2014, №2 (2), pp. 101-114

[13] Aksenov Ye.P., Grebenikov Ye.A., Demin V.G. The general solution of the problem of the motion of an artificial satellite in the Earth’s normal gravitational field. Planetary and space science, 1962, v. 9(8),, p. 491-498.

[14] Demin V.G. Dvizhenie iskustvennogo sputnika v netsentral’nom pole tyagoteniya. Moscow-Izhevsk, Regular and chaotic dynamics, 2010. 420 с.

[15] Vinti J.P. Theory of an accurate intermediate orbit for satellite astronomy. Nat. Bur. Standards. J. Res. Math. and Math. Physics, 1961, 65B, 2, p.169-201.

[16] Rodnikov A.V. On a particle motion along the leier fixed in a precessing rigid body. Rus. J. Nonlin. Dyn., 2011, т. 7. № 2. c. 295–311

[17] Rodnikov A.V. On coplanar equilibria of a space station on the cable fixed in an asteroid. Rus. J. Nonlin. Dyn., 2012. v. 8, № 2. p. 309–322

[18] Ivanov A.P. Dinamika system s mekhanicheskimi soudareniyami. Мoscow.: Mezhdunarodnaya programma obrazovaniya, 1997, 336 c.

[19] Rodnikov A.V. Coplanar libration points of the generalized restricted circular problem of three bodies for conjugate complex masses of attracting centers. Rus. J. Nonlin. Dyn., 2013, v. 9. № 4. p. 697–710

[20] Rodnikov A.V. Triangular Libration Points of the Generalized Restricted Circular Problem of Three Bodies for conjugate complex masses of attracting centers. Rus. J. Nonlin. Dyn., 2014, v. 10, № 2, p. 213–222

Rodnikov A. Modeling of a space station dynamics in vicinity of an asteroid. Маthematical Modeling and Coтputational Methods, 2016, №2 (10), pp. 55-68

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