Extensions to Chen’s minimizing equal mass parallelogram solutions. (English) Zbl 1444.70006

Summary: In this paper, we study the extension of the minimizing equal mass parallelogram solutions which was derived by K.-C. Chen [Arch. Ration. Mech. Anal. 158, No. 4, 293–318 (2001; Zbl 1028.70009)]. Chen’s solution was minimizing for one quarter of the period \([0,T]\), where numerical integration had been used in his proof. In this paper we extend Chen’s solution in the reduced space to \([0,4T]\) and we show that this extension is also minimizing over the intervals \([0,2T]\) and \([0,4T]\). The minimizing property of the extension is proved without using numerical integration.


70F10 \(n\)-body problems
34C25 Periodic solutions to ordinary differential equations
70H12 Periodic and almost periodic solutions for problems in Hamiltonian and Lagrangian mechanics


Zbl 1028.70009
Full Text: DOI Euclid


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