Abstract
The following theorem is proved. THEOREM.For any n≥2, the set of collinear relative equilibria classes of the n-body problem generates by analytical continuation a total of n!(n+3)/2 relative equilibria classes of the n+1 body problem.
Together with Arenstorf's results we state a general theorem for the 4 body problem with 3 arbitrary masses and 1 inferior mass.
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References
Arenstorf, R. F.: 1982, ‘Central Configurations of Four-Bodies with One Inferior Mass’,Celest. Mech. 28, 9 (this issue).
Palmore, J.: 1975, ‘Classifying Relative Equilibria, II’,Bull. Am. Math. Soc. 81, 489.
Palmore, J.: 1976, ‘Measure of Degenerate Relative Equilibria, I’,Ann. Math. 104, 421.
Palmore, J.: 1979, ‘Relative Equilibria and the Virial Theorem’,Celest. Mech. 19, 167.
Palmore, J.: 1981, ‘Central Configurations of the Restricted Problem inE 4’,J. Differential Equations 40, 291.
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Research supported in part by NSF grant MCS-78-00395 A01.
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Palmore, J.I. Collinear relative equilibria of the planarN-body problem. Celestial Mechanics 28, 17–24 (1982). https://doi.org/10.1007/BF01230656
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DOI: https://doi.org/10.1007/BF01230656