Stability of the Relative Equilibria in the Two-body Problem on the Sphere
Tóm tắt
We consider the 2-body problem in the sphere
$$\mathbb{S}^{2}$$
. This problem is modeled by a Hamiltonian system with
$$4$$
degrees of freedom and, following the approach given in [4], allows us to reduce the study to a system of
$$2$$
degrees of freedom. In this work we will use theoretical tools such as normal forms and some nonlinear stability results on Hamiltonian systems for demonstrating a series of results that will correspond to the open problems proposed in [4] related to the nonlinear stability of the relative equilibria. Moreover, we study the existence of Hamiltonian pitchfork and center-saddle bifurcations.
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