Abstract
We consider n bodies (with equal mass m) disposed at the vertices of a regular n-gon and rotating rigidly around an additional mass m 0(at its center) with a constant angular velocity (relative equilibrium). In the present paper, we prove results on the existence and on the linear stability of equilibrium positions for a zero-mass particle submitted to the gravitational field generated by the previous system.
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Bang, D. and Elmabsout, B.: 2001, Configurations polygonales en équilibre relatif, C.R.A.S., Paris, t.329, pp. 243–248.
Bang, D.A. and Elmabsout, B.: 2003, 'Representations of complex functions, means on the regular n-gon and applications to gravitational potential', Journals of Physics A, 36, 11435–11450.
Bass, J.: 1968, Cours de Mathématiques, I et II, Masson.
Elmabsout, B.: 1994, 'Stability of some degenerate positions of Relative Equilibrium in the n-body problem', Dynamics and Stability of Systems 9(4).
Lindow, M.: 1924, Der Kreisfall im Problem der n + 1 Korper, Astron. Nach.228, Kopenhagen, pp. 133–146.
Maxwell, J. C.: 1890, Stability of the Motion of Saturn's Rings, The scientific Papers of James Clerk Maxwell, Cambridge University Press.
Moeckel, R.: 1995, Linear Stability Analysis of some symmetrical Classes of Relative Equilibria, IMA, Vol. 63, Springer Verlag, NY.
Pedersen, P.: 1944, 'Librationspunkte im restringierten vierkorperproblem', Matematisk-fysiske Meddelelser bind XXI(6).
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Bang, D., Elmabsout, B. Restricted N+1-Body Problem: Existence and Stability Of Relative Equilibria. Celestial Mechanics and Dynamical Astronomy 89, 305–318 (2004). https://doi.org/10.1023/B:CELE.0000043568.88562.bf
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DOI: https://doi.org/10.1023/B:CELE.0000043568.88562.bf