Linear stability of relative equilibria in the charged three-body problem

Relative Equilibria of a Gyrostat in the Three Body Problem

We consider the non-canonical Hamiltonian dynamics of a gyrostat in the three body problem. By means of geometric-mechanics methods we will study the approximate dynamics that arises when we develop the potential in series of Legendre and truncate this in an arbitrary order. Working in the reduced problem, we will study the existence of relative equilibria that we will denominate of Euler and L...

Relative Equilibria in the Spherical, Finite Density Three-Body Problem

The relative equilibria for the spherical, finite density three-body problem are identified. Specifically, there are 28 distinct relative equilibria in this problem which include the classical five relative equilibria for the point-mass three-body problem. None of the identified relative equilibria exist or are stable over all values of angular momentum. The stability and bifurcation pathways o...

Bifurcations and Stability of Lagrangian Relative Equilibria for a Gyrostat in the Three Body Problem

In this paper we consider the non–canonical Hamiltonian dynamics of a gyrostat in the frame of the three body problem. Using geometric/mechanics methods we study the approximate dynamics of the truncated Legendre series representation of the potential of an arbitrary order. Working in the reduced problem, we study the existence of relative equilibria that we call of Lagrange type following the ...

Stability of relative equilibria of three vortices

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...