Zhang, Shiqing; Zhou, Qing A minimizing property of Lagrangian solutions. (English) Zbl 0988.70007 Acta Math. Sin., Engl. Ser. 17, No. 3, 497-500 (2001). This short paper shows that Lagrangian solutions of three-body problem minimize the action functional. The main result states that any minimal regular solution of the three-body problem is precisely the Lagrangian elliptic solution. The authors also give a brief review of Keplerian orbits and of the Gordon’s result. Reviewer: Nina A.Solovaya (Moskva) Cited in 1 ReviewCited in 20 Documents MSC: 70F07 Three-body problems Keywords:minimizing property; three-body problem; action functional; Lagrangian elliptic solution PDFBibTeX XMLCite \textit{S. Zhang} and \textit{Q. Zhou}, Acta Math. Sin., Engl. Ser. 17, No. 3, 497--500 (2001; Zbl 0988.70007) Full Text: DOI References: [1] R. Abraham, J. E. Marsden, Foundations of Mechanics, Benjamin/Cummings, 1978 · Zbl 0393.70001 [2] W. Gordon, A minimizing property of Keplerian orbits, Amer. J. of Math., 1977, 99:961–971 · Zbl 0378.58006 · doi:10.2307/2373993 [3] H. Pollard, Celestial Mechanics, The Mathematical Association of America, 1976 [4] J. Lagrange, Essai sur le probléme des trois crops, 1772, Ouvers, 1783, 3:229–331 [5] A. Chenciner, N. Desolneux, Minima de l’intégrale d’action etéquilibres relatifs de n corps, C. R. Acad. Sci. ParisI, serie, t.32, 1998, 1209–1212 · Zbl 0922.70009 [6] Y. Long, S. Q. Zhang, Geometric characterization for variational minimization solutions of the 3-body problem, Chinese Sci. Bull., 1999, 44:1653–1655 · Zbl 1288.70007 · doi:10.1007/BF03183482 [7] C. Siegel, J. Moser, Lectures on Celestial Mechanics, Berlin:Springer, 1971 · Zbl 0312.70017 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.