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The symmetric central configurations of four equal masses. (English) Zbl 0863.70012
Saari, Donald G. (ed.) et al., Hamiltonian dynamics and celestial mechanics. A joint summer research conference, June 25--29, 1995, Seattle, WA, USA. Providence, RI: American Mathematical Society. Contemp. Math. 198, 131-135 (1996).
Summary: In a relative equilibrium motion in the planar $n$-body problem, the configuration is called collinear central or planar central according to its dimension. We prove, by using a formal calculus program, that there are exactly three types of planar control configurations of four equal masses. For the entire collection see [Zbl 0851.00086].

70F10$n$-body problems
70H05Hamilton’s equations