Abstract
Orbit-orbit and spin-orbit gravitational resonances are analyzed using the model of a rigid pendulum subject to both a time-dependent periodic torque and a constant applied torque. First, a descriptive model of passage through resonance is developed from an examination of the polynomial equation that determines the extremes of the momentum variable. From this study, a probability estimate for capture into libration is derived. Second, a lowest order solution is constructed and compared with the solution obtained from numerical integration. The steps necessary to systematically improve this solution are also discussed. Finally, the effect of a dissipative term in the pendulum equation is analyzed.
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Yoder, C.F. Diagrammatic theory of transition of pendulum like systems. Celestial Mechanics 19, 3–29 (1979). https://doi.org/10.1007/BF01230171
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DOI: https://doi.org/10.1007/BF01230171