1978
DOI: 10.1007/bf01228714
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Relative equilibrium solutions in the four body problem

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Cited by 128 publications
(92 citation statements)
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“…We refer to this as the restricted four body problem (R4BP). There exist some preliminary studies of this problem in different versions, Simó (1978), Leandro (2006), Pedersen (1944) and Baltagiannis & Papadakis (2011b) studied the equilibrium points and their stability of this problem. Other authors have studied the case where the primaries form a collinear configuration.…”
Section: Accepted For Publication In Astrophysics and Space Sciencementioning
confidence: 99%
“…We refer to this as the restricted four body problem (R4BP). There exist some preliminary studies of this problem in different versions, Simó (1978), Leandro (2006), Pedersen (1944) and Baltagiannis & Papadakis (2011b) studied the equilibrium points and their stability of this problem. Other authors have studied the case where the primaries form a collinear configuration.…”
Section: Accepted For Publication In Astrophysics and Space Sciencementioning
confidence: 99%
“…In 1975, Palmore [25] gave a simple example of a degenerate central configuration, an equilateral triangle of bodies with unit mass and a fourth body with mass (64 √ 3+81)/249 at the center of the triangle. Simó [28] showed how the number of 4-body central configurations with a given body in the interior of the triangle formed by the other bodies varies when the four masses vary. Xia [34] proved that in the n-body problem, the relative equilibria may be counted exactly for several 1 [5] was published a few weeks after the end of first world war.…”
Section: Introduction and Statementsmentioning
confidence: 99%
“…A numerical study for the number of central configurations for N = 4 and arbitrary masses was done by Simó in [39]. In a computer assisted proof Hampton and Moeckel [21] proved the finiteness of the number of central configurations for N = 4 and any choice of the masses.…”
mentioning
confidence: 99%