Abstract
Using the local asymmetric expansion of the disturbing function for the planar elliptic restricted three-body problem up to degree 1 ine 1 we develop a small amplitude libration theory. We review the laws that characterize the mean-motion resonances of asteroids with Jupiter and we obtain other new laws. Special attention is paid to the second forced mode whose equations are reformulated and new consequences of this component are discussed. An analytical expression for the trajectories in the phase space is obtained. The predictions are compared with numerical experiments which confirm the results.
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Gallardo, T., Ferraz-Mello, S. The high-eccentricity libration theory revisted. Celestial Mech Dyn Astr 62, 145–165 (1995). https://doi.org/10.1007/BF00692084
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DOI: https://doi.org/10.1007/BF00692084