Abstact
In the planetary form of the three-body problem for first-order resonances the qualitative studies of the evolution of orbital elements of gravitating bodies’ were carried out taking into account the Rayleigh dissipation. The stationary solutions were considered and the phase trajectories were classified. The expressions for the deviation of orbital parameters were obtained.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Chirikov, B.A., Universal instability of many dimensional oscillator system, Phys. Reports, 1979, vol. 59, pp. 263–279.
Abramowitz, M. and I. A. Stegun, I.A., Handbook of Mathematical Functions, Dover, New York: 1965. Translated under the title Spravochnik po spetsial’nym funktsiyam, Moscow: Nauka, 1979.
Gerasimov, I.A. and Mushailov, B.R., Some issues of dynamical evolution of small bodies of the Solar System, Preprint of Sternberg State Astron. Inst., Moscow State Univ., Moscow, 1992, no. 27.
Gerasimov, I.A., Mushailov, B.R., and Rakitina, N.V., Qualitative studies of motions in the restricted elliptical three body problem at first-order commensurability, Astron. Vestn., 1994, vol. 28, no. 4–5, pp. 186–200.
Gerasimov, I.A. and Mushailov, B.R., Investigation of dynamical characteristics of orbits in the three body problem at resonances of the first order, Astron. Vestn., 1995, vol. 29, no. 1, pp. 58–66.
Gerasimov, I.A. and Mushailov, B.R., Analytical solution of generalized three body problem at first-order commensurability, Astron. Vestn., 1995, vol. 29, no. 1, pp. 67–71.
Gerasimov, I.A. and Mushailov, B.R., Resonance multiplicity in a three-body problem, Kosm. Issled., 1995, vol. 33, no. 1, pp. 109–110. (Cosmic Research, pp. 100–101).
Gerasimov, I.A. and Mushailov, B.R., Partial analytical solutions in the three body problem at first-order commensurability, Astron. Vestn., 1996, vol. 30, no. 1, pp. 92–96.
Zaslavskii, G.M., Sagdeev, R.Z., Usikov, D.A., and Chernikov, A.A., Slabyi khaos i kvaziregulyarnye struktury (Weak Chaos and Quasi-Regular Structures), Moscow: Nauka, 1991.
Kravtsov, Yu.A., Randomness, determinacy, and predictability, Usp. Fiz. Nauk, 1989, vol. 158, no. 1, pp. 93–122.
Martynova, A.I. and Orlov, V.L., Resonances in the problem of three bodies with different masses, Astron. Zh., 2011, vol. 88, no. 2, pp. 196–203.
Mushailov, B.R., Evolution of the Uranus-Neptune system, Astron. Vestn., 1995, vol. 29, no. 4, pp. 375–384.
Mushailov, B.R. and Gerasimov, I.A., Evolution of orbits in the system of Saturn’s moons Enceladus and Dione, Astron. Vestn., 1996, vol. 30, no. 4, pp. 355–367.
Mushailov, B.R. and Teplitskaya, V.S., Analytical solutions interpreting the evolution of two-frequency space systems in the case of Lindblad resonance with allowance made for Raleigh dissipation, to be published.
Simo, K., Sovremennye problemy khaosa i nelineinosti (Modern problems of chaos and nonlinearity), Izhevsk: Izd. Inst. komp’yuternykh issledovanii, 2002.
Author information
Authors and Affiliations
Additional information
Original Russian Text © B.R. Mushailov, V.S. Teplitskaya, 2013, published in Kosmicheskie Issledovaniya, 2013, Vol. 51, No. 5, pp. 402–411.
Rights and permissions
About this article
Cite this article
Mushailov, B.R., Teplitskaya, V.S. Qualitative studies of orbital elements evolution in the planetary resonance form of the three-body problem in the case of the Rayleigh dissipation. Cosmic Res 51, 362–371 (2013). https://doi.org/10.1134/S0010952513050079
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0010952513050079