The main mean motion commensurabilities in the planar circular and elliptic problem |
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Authors: | Michèle Moons Alessandro Morbidelli |
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Affiliation: | (1) Département de mathématique FUNDP, 8, Rempart de la Vierge, B-5000 Namur, Belgique |
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Abstract: | We study the motion of asteroids in the main mean motion commensurabilities in the frame of the planar restricted three-body problem. No assumption is made about the size of the eccentricity of the asteroid. At small to moderate eccentricity, we recover existing results (shape of the phase space and location of secondary resonances). We also provide global pictures of the dynamics in the region of secondary resonances. At high eccentricity, the phase space portraits of the integrable part of the Hamiltonian show new families of stable orbits for the 3:2 and 2:1 cases and the secular resonances 5 and 6 are located. |
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Keywords: | mean motion resonances secondary resonances secular resonances planar circular and elliptic restricted problem action-angle variables surfaces of section |
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