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Zbl 0863.70012
Albouy, Alain
The symmetric central configurations of four equal masses. (English)
[A] 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). ISBN 0-8218-0566-5/pbk

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.

MSC 2000:: *70F10 n-body problem
70H05 Hamilton's equations

Keywords: collinear central configuration; relative equilibrium motion; formal calculus program; planar control configurations

Cited in: Zbl 1157.70008 Zbl 0984.70010 Zbl 1004.70008

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