Action minimizing orbits in the 2-center problems with simple choreography constraint

2019/11/05 by Zhao, Furong, Wang, Zhiqiang
#34C25 #70F10 #70G75 #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1911.01566

Abstract

The aim of this paper is to study the motion of 2+n-body problem where two equal masses are assumed to be fixed. We assume that the value of each fixed mass is equal to M>0 and the remaining n moving particles have equal masses m>0. According to Newton's second law and the universal gravitation law, the n particles move under the interaction of each other and the affection of the two fixed particles. Also, this motion has a natural variational structure. Under the simple choreography constraint, we show that the Lagrangian action functional attains its absolute minimum on a uniform circular motion.

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