Abstract
This paper studies the existence and stability of equilibrium points under the influence of small perturbations in the Coriolis and the centrifugal forces, together with the non-sphericity of the primaries. The problem is generalized in the sense that the bigger and smaller primaries are respectively triaxial and oblate spheroidal bodies. It is found that the locations of equilibrium points are affected by the non-sphericity of the bodies and the change in the centrifugal force. It is also seen that the triangular points are stable for 0<μ<μ c and unstable for \(\mu_{c}\le\mu <\frac{1}{2}\), where μ c is the critical mass parameter depending on the above perturbations, triaxiality and oblateness. It is further observed that collinear points remain unstable.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Abdul Raheem, A., Singh, J.: Astron. J. 131, 1880 (2006)
Bhatnagar, K.B., Hallan, P.P.: Celest. Mech. 18, 105 (1978)
Bhatnagar, K.B., Hallan, P.: Celest. Mech. Dyn. Astron. 20, 95 (1979)
Chandra, N., Kumar, R.: Astrophys. Space Sci. 291, 1 (2004)
Contopoulos, G.: Order and Chaos in Dynamical Astronomy, p. 543. Springer, Berlin (2002)
Elipe, A.: Astrophys. Space Sci. 188, 257 (1992)
El-Shaboury, S.M.: Celest. Mech. Dyn. Astron. 50, 199 (1991)
Kalantonis, V.S., Perdios, E.A., Perdiou, A.E., Vrahatis, M.N.: Celest. Mech. Dyn. Astron. 80, 81 (2001)
Kavvadias, D.J., Vrahatis, M.N.: SIAM J. Sci. Comput. 17, 1232 (1996)
McCusky, S.W.: Introduction to Celestial Mechanics. Addison-Wesley, New York (1963)
Picard, E.: J. Math. Pure Appl. 8, 5 (1892)
Picard, E.: Traite D’analyse, 3rd edn. Gauthier-Villars, Paris (1922) Chap. 4.7
Sharma, R.K., Taqvi, Z.A., Bhatnagar, K.B.: Celest. Mech. Dyn. Astron. 79, 119 (2001)
Singh, J.: Astron. J. 137, 3286 (2009)
Subbarao, P.V., Sharma, R.K.: Astron. Astrophys. 43, 381 (1975)
Szebehely, V.: Astron. J. 72, 7 (1967a)
Szebehely, V.: Theory of Orbits: The Restricted Problem of Three Bodies, pp. 244–264. Academic Press, New York (1967b)
Vidyakin, V.V.: Astron. Zh. 51(5), 1087 (1974)
Wintner, A.: The Analytical Foundation of Celestial Mechanics, pp. 372–373. Princeton University Press, Princeton (1941)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Singh, J., Begha, J.M. Stability of equilibrium points in the generalized perturbed restricted three-body problem. Astrophys Space Sci 331, 511–519 (2011). https://doi.org/10.1007/s10509-010-0464-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10509-010-0464-1