Miusskaya sq. 4, Moscow, 125047, Russia
M. V. Keldysh Institute for Applied Mathematics, Russian Academy of Sciences
Beletsky V. V., Kugushev E. I., Starostin E. L.
Free manifolds of dynamic billiards
1997, vol. 2, nos. 3-4, pp. 62-71
We consider free manifolds of dynamic billiards that allow constructing mathematical billiards equivalent to original dynamic billiards. It is shown that free manifolds of dynamic billiards in constant and Newtonian force field are surfaces of rotation in 3D Euclidean space. It is demonstrated that parabolic billiards in Newtonian attracting force field are equivalent to plane mathematical billiards.
Beletsky V. V., Salimova O. P.
Hill's Problem as a Dynamical Billiard
1996, vol. 1, no. 2, pp. 47-58
A problem of a mass point movements in gravitation field of two selestial body, one of which has small size and mass with respect to the other and is situated in its immediate proximity, is considered in the paper. Substantively, such model can describe movement of an apparatus in Mars-Fobos system. Movement of robot near the surface of a satellite in its umbilical orbit plane has been numerically analyzed by means of Poincare cut method within the scope of classical Hill problem. The domains of chaotic movements of the problem have been found and new periodical orbits have been shown.
Beletsky V. V., Pankova D. V.
Connected Bodies in the Orbit as Dynamic Billiard
1996, vol. 1, no. 1, pp. 87-103
There is discussed one billiard problem describing an interaction of two mass points united by an non-extensible weightless thread the center of mass of which moves along the circular Kepler orbit. There have been built phase portraits of Poincare's maps and found the fields of the regular behavior of the system.