Abstract
The effect of small perturbations ε and ε ′ in the Coriolis and the centrifugal forces, respectively on the nonlinear stability of the triangular points in the restricted three-body problem with variable mass has been studied. It is found that, in the nonlinear sense, the triangular points are stable for all mass ratios in the range of linear stability except for three mass ratios, which depend upon ε, ε ′ and β, the constant due to the variation in mass governed by Jeans’ law.
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References
AbdulRaheem, A., Singh, J.: Astron. J. 131, 1880 (2006)
Arnold, V.I.: Soviet Math. Dokl. 2, 247 (1961)
Bekov, A.A.: Instability, Chaos and Predictability in Celestial Mechanics and Stellar Dynamics, p. 277. Nova Science Publishers, New York (1992)
Bhatnagar, K.B., Hallan, P.P.: Celest. Mech. 18, 105 (1978)
Contopoulos, G.: Order and Chaos in Dynamical Astronomy, p. 543. Springer, Berlin (2002)
Deprit, A., Deprit Bartholome, A.: Astron. J. 72, 173 (1967)
Gozdziewski, K.: Celest. Mech. Dyn. Astron. 85, 79 (2003)
Hallan, P.P., Jain, S., Bhatnagar, K.B.: Celest. Mech. Dyn. Astron. 77, 157 (2000)
Ishwar, B.: Celest Mech. Dyn. Astron. 65, 253 (1997)
Jeans, J.H.: Astronomy and Cosmogony. Cambridge University Press, London (1928)
Liapunov, A.M.: A General Problem of Stability of Motion. Acad. Sci. USSR, Moscow (1956)
Meshcherskii, I.V.: Studies on the Mechanics of Bodies of Variable Mass. Moscow, Leningrad (1949)
Moser, J.K.: Nachr. Akad. Wiss. Gottingen, Math-Phys. KI, 1 (1962)
Niedzielska, Z.: Celest. Mech. Dyn. Aston. 58, 203 (1994)
Shrivastava, A.K., Ishwar, B.: Celest. Mech. 30, 323 (1983)
Singh, J., Ishwar, B.: Celest. Mech. 32, 297 (1984)
Singh, J., Ishwar, B.: Celest. Mech. 35, 201 (1985)
Subbarao, P.V., Sharma, R.K.: Astron. Astrophys. 43, 381 (1975)
Subbarao, P.V., Sharma, R.K.: Celest. Mech. Dyn. Astron. 65, 291 (1997)
Szebehely, V.: Theory of Orbits: The Restricted Problem of Three Bodies, pp. 244–264. Academic Press, New York (1967a)
Szebehely, V.: Astron. J. 72, 7 (1967b)
Verhulst, F.: Celest. Mech. 5, 27 (1972)
Whittaker, E.T.: A Treatise on the Analytical Dynamics of Particles and Rigid Bodies, pp. 427–430. Cambridge University Press, London (1965)
Wintner, A.: The Analytical Foundations of Celestial Mechanics, pp. 372–373. Princeton University Press, Princeton (1941)
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Singh, J. Effect of perturbations on the non linear stability of triangular points in the restricted three-body problem with variable mass. Astrophys Space Sci 321, 127–135 (2009). https://doi.org/10.1007/s10509-009-0018-6
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DOI: https://doi.org/10.1007/s10509-009-0018-6