Linear stability of the elliptic relative equilibrium with $ (1 + 7) $-gon central configuration in planar $ N $-body problem

Planar Central Configuration Estimates in the N-body Problem

For all masses, there are at least n ?2 O 2-orbits of non-collinear planar central conngurations. In particular, this estimate is valid even if the potential function is not a Morse function. If the potential function is a Morse function, then an improved lower bound, on the order of n! ln ? n+1 3 =2, can be given.

Stability of Relative Equilibria in the Planar n-Vortex Problem

We study the linear and nonlinear stability of relative equilibria in the planar n-vortex problem, adapting the approach of Moeckel from the corresponding problem in celestial mechanics. After establishing some general theory, a topological approach is taken to show that for the case of positive circulations, a relative equilibrium is linearly stable if and only if it is a nondegenerate minimum...

Central configurations and relative equilibria in the n–body problem

Linear stability and resonance of triangular equilibrium points in elliptic restricted three body problem with radiating primary and triaxial secondary

The present paper studies the linear stability of the triangular equilibrium points of the system. The system comprises of a radiating primary and a triaxial secondary in elliptic restricted three body problem. The existence of third order resonances has been shown and the linear stability has been analyzed for these resonance cases. For the resonance case, 3λ2 = 1 and 2λ1 + λ2 = 0, the conditi...

Finiteness of Relative Equilibria in the Planar Generalized N-body Problem with Fixed Subconfigurations

We prove that a fixed configuration of N − 1 masses in the plane can be extended to a central configuration of N masses by adding a specified additional mass only in finitely many ways. This holds for a family of potential functions including the Newtonian gravitational case and the classical planar point vortex model.