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arXiv · 1910.00367

Eulerian collinear configuration for 3-body problem

Liang Ding·Juan Manuel Sánchez-Cerritos·Jinlong Wei
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Abstract

For 3-body problem with any given masses $m_1, \,m_2,\,m_3>0$, there exist only Eulerian collinear central configuration and Lagrangian equilateral-triangle central configuration, and in this paper, for planar 3-body problem, we prove that there exists another non-collision trajectory $q$, which is not the variational minimizer of the Lagrangian action on the loop space $\overline{\Lambda_1}$, is also an Eulerian collinear central configuration at any instant. Moreover, we do not need the restriction condition on the winding number $deg(q_i-q_j)\neq0 \,(i\neq j)$.

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Liang Ding, Juan Manuel Sánchez-Cerritos, Jinlong Wei. 2019-10-01. Eulerian collinear configuration for 3-body problem. https://arxiv.org/abs/1910.00367

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