Jaime Andrade
Publications:
Andrade J., Vidal C.
Stability of the Polar Equilibria in a Restricted Threebody Problem on the Sphere
2018, vol. 23, no. 1, pp. 80101
Abstract
In this paper we consider a symmetric restricted circular threebody problem on the surface $\mathbb{S}^2$ of constant
Gaussian curvature $\kappa=1$. This problem consists in the description of the dynamics of an infinitesimal mass particle attracted
by two primaries with identical masses, rotating with constant angular velocity in a fixed parallel of radius $a\in (0,1)$.
It is verified that both poles of $\mathbb{S}^2$ are equilibrium points for any value of the parameter $a$. This problem is
modeled through a Hamiltonian system of two degrees of freedom depending on the parameter $a$. Using results concerning nonlinear
stability, the type of Lyapunov stability (nonlinear) is provided for the polar equilibria, according to the resonances.
It is verified that for the north pole there are two values of bifurcation (on the stability) $a=\dfrac{\sqrt{4\sqrt{2}}}{2}$ and $a=\sqrt{\dfrac{2}{3}}$,
while the south pole has one value of bifurcation $a=\dfrac{\sqrt{3}}{2}$.
