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This article is cited in 1 scientific paper (total in 1 paper)
Stability of the Polar Equilibria in a Restricted Three-body Problem on the Sphere
Jaime Andrade, Claudio Vidal Universidad de Bío-Bío, Grupo de Investigación en Sistemas Dinámicos y Aplicaciones-GISDA, Casilla 5–C, Concepción, VIII–región, Chile
Abstract:
In this paper we consider a symmetric restricted circular three-body 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 $a=\dfrac{\sqrt{3}}{2}$.
Keywords:
circular restricted three-body problem on surfaces of constant curvature, Hamiltonian formulation, normal form, resonance, nonlinear stability.
Received: 01.10.2017 Accepted: 05.12.2017
Citation:
Jaime Andrade, Claudio Vidal, “Stability of the Polar Equilibria in a Restricted Three-body Problem on the Sphere”, Regul. Chaotic Dyn., 23:1 (2018), 80–101
Linking options:
https://www.mathnet.ru/eng/rcd310 https://www.mathnet.ru/eng/rcd/v23/i1/p80
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Abstract page: | 623 | References: | 36 |
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