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The spin-orbit resonances of the solar system: a mathematical treatment matching physical data. (English) Zbl 1302.70034
Summary: In the mathematical framework of a restricted, slightly dissipative spin-orbit model, we prove the existence of periodic orbits for astronomical parameter values corresponding to all satellites of the Solar System observed in exact spin-orbit resonance.

MSC:
70F15 Celestial mechanics
70F40 Problems involving a system of particles with friction
70E20 Perturbation methods for rigid body dynamics
70G70 Functional analytic methods for problems in mechanics
70H09 Perturbation theories for problems in Hamiltonian and Lagrangian mechanics
70H12 Periodic and almost periodic solutions for problems in Hamiltonian and Lagrangian mechanics
34C23 Bifurcation theory for ordinary differential equations
34C25 Periodic solutions to ordinary differential equations
34C60 Qualitative investigation and simulation of ordinary differential equation models
34D10 Perturbations of ordinary differential equations
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