Central Configurations and Total Collisions for Quasihomogeneous n-Body Problems

Abstract

We consider $n$-body problems given by potentials of the form $\frac{\alpha }{r^a}+\frac{\beta }{r^b}$ with $a,b,\alpha ,\beta$ 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.

References in corpus (1)

• Saari's Conjecture for the Collinear $n$-Body Problem

Cited by in corpus (4)

• Dynamics in the Schwarzschild isosceles three body problem
• Existence of a lower bound for the distance between point masses of relative equilibria for generalised quasi-homogeneous $n$-body problems and the curved $n$-body problem
• Relative equilibria in quasi-homogeneous three body problems
• Equal masses results for choreographies $n$-body problems