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arXiv · 0909.4989

Central Configurations and Total Collisions for Quasihomogeneous n-Body Problems

Florin Diacu·Ernesto Perez-Chavela·Manuele Santoprete
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Abstract

We consider $n$-body problems given by potentials of the form ${α\over r^a}+{β\over r^b}$ with $a,b,α,β$ constants, $0\le a<b$. To analyze the dynamics of the problem, we first prove some properties related to central configurations, including a generalization of Moulton's theorem. Then we obtain several qualitative properties for collision and near-collision orbits in the Manev-type case $a=1$. At the end we point out some new relationships between central configurations, relative equilibria, and homothetic solutions.

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Florin Diacu, Ernesto Perez-Chavela, Manuele Santoprete. 2009-09-28. Central Configurations and Total Collisions for Quasihomogeneous n-Body Problems. https://doi.org/10.1016/j.na.2005.10.023

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