On the uniqueness of the planar 5-body central configuration with a trapezoidal convex hull

2023/05/02 by Liu, Yangshanshan, Zhang, Shiqing
#37N05 #70F10 #70F15 #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2305.01376

Abstract

To apply Morse's critical point theory, we use mutual distances as coordinates to discuss a kind of central configuration of the planar Newtonian 5-body problem with a trapezoidal convex hull, i.e., four of the five bodies are located at the vertices of a trapezoid, and the fifth one is located on one of the parallel sides. We show that there is at most one central configuration of this geometrical shape for a given cyclic order of the five bodies along the convex hull.

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