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arXiv · 1911.01566

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

Furong Zhao·Zhiqiang Wang
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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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Furong Zhao, Zhiqiang Wang. 2019-11-05. Action minimizing orbits in the 2-center problems with simple choreography constraint. https://arxiv.org/abs/1911.01566

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