Perturbations in coriolis and centrifugal forces and N-R basins of convergence of photogravitational magnetic-binary problem with variable mass
Heading:
| Kumar, V, KumarMarig, S |
| Kinemat. fiz. nebesnyh tel (Online) 2023, 39(6):36-57 |
| https://doi.org/10.15407/kfnt2023.06.036 |
| Language: Ukrainian |
Abstract: In this paper, we have investigated the effect of small perturbations in the Coriolis (φ) and centrifugal (ψ) forces in the photogravitational magnetic binary problem including the effect of third body as variable mass. The objective of this work is to analyse the effect of and other parameters (magnetic moments λ and radiation pressure q) on the existence and evolution of equilibrium points, basins of convergence (BoC), degree of unpredictability in BoC. In addition, to examine the effect of and (in the presence of other parameters) on the stability of equilibrium points are also one of the aspect of this work. For different values of parameters, a total number of cases of non-collinear equilibrium points are 3, 5 and 7. The effect of various parameters on the evolution of equilibrium points are explained with the help of graphs. All non-collinear equilibrium points are found to be unstable for permissible range of parameters present in this model. The change in geometry of BoC’s is also shown and explained using graphs. The effect of ψ , q and λ on the degree of unpredictability in BoC’s is examined using the method of basin entropy. It is found that for the complete range of λ and q, the BoC’s are in fractal region. Also, for the values of ψ = 1.37, 1.38 and 1.40 to 1.44, the boundaries of BoC’s are in non-fractal region. |
| Keywords: basin entropy, basin of convergence, centrifugal force, Coriolis force, magnetic binary problem |
References:
1. Aggarwal R., Mittal A., Suraj M. S., Bisht V. (2018). The effect of small perturbations in the Coriolis and centrifugal forces on the existence of libration points in the restricted four-body problem with variable mass. Astron. Nachr. 339(6). 492-512. https://doi.org/10.1002/asna.201813411
2. Bhatnagar K. B., Hallan P. P. (1978). Effect of perturbations in Coriolis and centrifugal forces on the stability of libration points in the restricted problem. Celestial Mech. 18(2). 105-112. https://doi.org/10.1007/BF01228710
3. Bhatnagar K. B., Hallan P. P. (1983). The effect of perturbations in Coriolis and centrifugal forces on the nonlinear stability of equilibrium points in the restricted problem of three bodies. Celestial Mech. 30(1). 97-114. https://doi.org/10.1007/BF01231105
4. Daza A., Bertrand G., Guery-Odelin D., Wagemakers A., Sanjuan M. A. F. (2017). Chaotic dynamics and fractal structures in experiments with cold atoms. Phys. Rev. A. 95(1), 013629. https://doi.org/10.1103/PhysRevA.95.013629
5. Daza A., Wagemakers A., Georgeot B., Guery-Odelin D., Sanjuan M. A. F. (2016). Basin entropy: a new tool to analyze uncertainty in dynamical systems. Sci. Rep. 6(1), 31416. https://doi.org/10.1038/srep31416
6. Idrisi M. J., Ullah M. S., Sikkandhar A. (2021). Effect of perturbations in Coriolis and centrifugal forces on libration points in the restricted Six-Body problem. J. Astronaut. Sci. 68(1), 4-25. https://doi.org/10.1007/s40295-021-00254-3
7. Jeans J. H. (1928). Astronomy and cosmogony, Cambridge University. https://doi.org/10.1017/S0016756800107861
8. Kumar V., Arif M., Ullah M. S. (2021). Capricious basins of attraction in photogravitational magnetic binary problem. New Astron. 83, 101475. https://doi.org/10.1016/j.newast.2020.101475
9. Kumar V., Idrisi M. J., Ullah M. S. (2021). Unpredictable basin boundaries in restricted six-body problem with square configuration. New Astron. 82, 101451. https://doi.org/10.1016/j.newast.2020.101451
10. Kumar V., Marig S. K. (2023). Effect of variable mass on N-R basins of con¬vergence in photogravitational magnetic binary problem. Astron. Reps. 67(2), 194-208. https://doi.org/10.1134/S1063772923020105
11. Kumar V., Sharma P., Aggarwal R., Yadav S., Kaur B. (2020). The unpredictability of the basins of attraction in photogravitational Chermnykh's problem. Astrophys. and Space Sci. 365(6), 1-19. https://doi.org/10.1007/s10509-020-03815-4
12. Meshcherskii I. V. (1949). Study on the mechanics of bodies of variable mass. Moscow.
13. Shrivastava A. K., Ishwar B. (1983). Equations of motion of the restricted problem of three bodies with variable mass. Celestial Mech. 30(3), 323-328. https://doi.org/10.1007/BF01232197
14. Singh J., Ishwar B. (1984). Effect of perturbations on the location of equilibrium points in the restricted problem of three bodies with variable mass. Celestial Mech. 32(4), 297-305. https://doi.org/10.1007/BF01229086
15. Singh J., Ishwar B. (1985). Effect of perturbations on the stability of triangular points. In the restricted problem of three bodies with variable mass. Celestial Mech. 35(3), 201-207. https://doi.org/10.1007/BF01227652
16. Singh J., Vincent A. E. (2015). Effect of perturbations in the Coriolis and centrifugal forces on the stability of equilibrium points in the restricted four-body problem. Few-Body Syst. 56(10), 713-723. https://doi.org/10.1007/s00601-015-1019-3
17. Suraj M. S., Aggarwal R., Arora M. (2017). On the restricted four-body problem with the effect of small perturbations in the Coriolis and centrifugal forces. Astrophys. and Space Sci. 362(9), 1-11. https://doi.org/10.1007/s10509-017-3123-y
18. Suraj M. S., Aggarwal R., Asique M. C., Mittal A. (2021). On the basins of convergence in the magnetic-binary problem with angular velocity. Comput. and Math. Meth. 3(4), e1161. https://doi.org/10.1002/cmm4.1161
19. Suraj M. S., Sachan P., Mittal A., Aggarwal R. (2019). The effect of small perturbations in the Coriolis and centrifugal forces in the axisymmetric restricted five-body problem. Astrophys. and Space Sci. 364(3), 1-13. https://doi.org/10.1007/s10509-019-3528-x
20. Szebehely V. (1967). Stability of the points of equilibrium in the restricted problem. Astron. J. 72, 7. https://doi.org/10.1016/B978-0-12-395732-0.50007-6
21. Wintner A. (1941). The analytical foundations of celestial mechanics. Princeton. https://doi.org/10.1038/149534a0
22. Wolfram Research, Inc. (2019), Mathematica, Version 12.0, Champaign, IL.
23. Zotos E. E. (2017). Determining the Newton-Raphson basins of attraction in the electro¬magnetic Copenhagen problem. Int. J. Non-Linear Mech. 90, 111-123. https://doi.org/10.1016/j.ijnonlinmec.2017.01.009
24. Zotos E. E., Abouelmagd E. I., Abd E1 Motelp N. S. (2020). Introducing a new version of the restricted three-body problem with a continuation fraction potential. New Astron. 81, 101444. https://doi.org/10.1016/j.newast.2020.101444
25. Zotos E. E., Chen W., Abouelmagd E. I., Han H. (2020). Basins of convergence of equilibrium points in the restricted three-body problem with modified gravitational potential. Chaos, Solitons and Fractals. 134. 109704. https://doi.org/10.1016/j.chaos.2020.109704