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Analysis of resonances in the spin-orbit problem in celestial mechanics. II: Higher order resonances and some numerical experiments. (English) Zbl 0711.70016
Summary: [For part I see ibid. 41, 174-204 (1990; Zbl 0699.70014).]
We study the stability of the nonsynchronous resonances in the spin-orbit problem in Celestial Mechanics. Using a mathematical model obtained making some restrictions on the physical problem, we trap the 3:2 resonance between invariant surfaces for realistic values of the physical and orbital parameters in the cases of the Moon and other three satellites of Saturn. We also provide some remarks on higher order resonances and on the Mercury-Sun system. Moreover we apply some numerical techniques in order to determine the break-down threshold of the invariant tori. In the last section we give some remarks on the robustness of the golden mean torus.

MSC:
70F15 Celestial mechanics
70K30 Nonlinear resonances for nonlinear problems in mechanics
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