Abstract
The aim of this paper is to study the motion of a \(2+n\)-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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Acknowledgements
The first author was supported by The Youth Fund of Mianyang Normal University and Project of Sichuan Education Department, and the second author was supported by the National Natural Science Foundation of China (11601045) and China Scholarship Council. Part of this work was done when the second author was visiting University of Minnesota. He thanks the School of Mathematics and Professor Richard Moeckel for their hospitality and support.
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Zhao, F., Wang, Z. Action Minimizing Orbits in the 2-Center Problems with Simple Choreography Constraint. Few-Body Syst 63, 78 (2022). https://doi.org/10.1007/s00601-022-01779-5
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DOI: https://doi.org/10.1007/s00601-022-01779-5