Abstract
We discuss the equilibrium solutions of four different types of collinear four-body problems having two pairs of equal masses. Two of these four-body models are symmetric about the center-of-mass while the other two are non-symmetric. We define two mass ratios as μ 1 = m 1/M T and μ 2 = m 2/M T, where m 1 and m 2 are the two unequal masses and M T is the total mass of the system. We discuss the existence of continuous family of equilibrium solutions for all the four types of four-body problems.
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References
Arenstrof, R. F. 1982, Celest. Mech., 28, 9–15.
Douskos, C. N. 2010, Astrophys. Space Sci., 326, 263–271.
Glass, K. 1997, Phys. Lett., A235, 591–596.
Gomatan, J., Steves, B. A., Roy, A. E. 1999, “The Dynamics of Small Bodies in the Solar System: A Major Key to Solar System Studies”, (eds) Steves B. A., Roy A. E., pp. 373–378.
Kozak, D., Oniszk, E. 1998, Romanian Astron. J., 8(1), 27–31.
Majorana, A. 1981, Celest. Mech., 25, 267–270.
Moulton, F. 1910, Ann. Math., 12, 1–15.
Murray, C. D., Dermot, S. F. 1999, Solar System Dynamics, Cambridge University Press.
Ouyang, T., Xie, Z. 2005, Celest. Mech. Dynamical Astron., 93, 147–166.
Palmore, J. 1975, Bull. Amer. Math. Soc., 81, 489.
Palmore, J. 1982, Celest. Mech., 28, 17–24.
Roy, A. E., Steves, B. A. 1998, Planet. Space Sci., 46(11/12), 1475–1486.
Zhiming, Y., Yisui, S. 1988, Scientia Sinica, XXXI(6), 724–733.
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Shoaib, M., Faye, I. Collinear Equilibrium Solutions of Four-body Problem. J Astrophys Astron 32, 411–423 (2011). https://doi.org/10.1007/s12036-011-9088-2
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DOI: https://doi.org/10.1007/s12036-011-9088-2