Stable Manifolds and Homoclinic Points Near Resonances in the Restricted Three-Body Problem
dc.contributor.author | Viswanath, Divakar | en_US |
dc.date.accessioned | 2006-09-08T20:29:05Z | |
dc.date.available | 2006-09-08T20:29:05Z | |
dc.date.issued | 2006-02 | en_US |
dc.identifier.citation | Viswanath, D.; (2006). "Stable Manifolds and Homoclinic Points Near Resonances in the Restricted Three-Body Problem." Celestial Mechanics and Dynamical Astronomy 94(2): 213-235. <http://hdl.handle.net/2027.42/42571> | en_US |
dc.identifier.issn | 0923-2958 | en_US |
dc.identifier.issn | 1572-9478 | en_US |
dc.identifier.uri | https://hdl.handle.net/2027.42/42571 | |
dc.description.abstract | The restricted three-body problem describes the motion of a massless particle under the influence of two primaries of masses 1− μ and μ that circle each other with period equal to 2π. For small μ, a resonant periodic motion of the massless particle in the rotating frame can be described by relatively prime integers p and q , if its period around the heavier primary is approximately 2π p / q , and by its approximate eccentricity e . We give a method for the formal development of the stable and unstable manifolds associated with these resonant motions. We prove the validity of this formal development and the existence of homoclinic points in the resonant region. In the study of the Kirkwood gaps in the asteroid belt, the separatrices of the averaged equations of the restricted three-body problem are commonly used to derive analytical approximations to the boundaries of the resonances. We use the unaveraged equations to find values of asteroid eccentricity below which these approximations will not hold for the Kirkwood gaps with q / p equal to 2/1, 7/3, 5/2, 3/1, and 4/1. Another application is to the existence of asymmetric librations in the exterior resonances. We give values of asteroid eccentricity below which asymmetric librations will not exist for the 1/7, 1/6, 1/5, 1/4, 1/3, and 1/2 resonances for any μ however small. But if the eccentricity exceeds these thresholds, asymmetric librations will exist for μ small enough in the unaveraged restricted three-body problem. | en_US |
dc.format.extent | 238043 bytes | |
dc.format.extent | 3115 bytes | |
dc.format.mimetype | application/pdf | |
dc.format.mimetype | text/plain | |
dc.language.iso | en_US | |
dc.publisher | Kluwer Academic Publishers; Springer | en_US |
dc.subject.other | Physics | en_US |
dc.subject.other | Astronomy | en_US |
dc.subject.other | Asymmetric Libration | en_US |
dc.subject.other | Homoclinic Points | en_US |
dc.subject.other | Kirkwood Gaps | en_US |
dc.subject.other | Resonance | en_US |
dc.subject.other | Three-body Problem | en_US |
dc.title | Stable Manifolds and Homoclinic Points Near Resonances in the Restricted Three-Body Problem | en_US |
dc.type | Article | en_US |
dc.subject.hlbsecondlevel | Astronomy | en_US |
dc.subject.hlbtoplevel | Science | en_US |
dc.description.peerreviewed | Peer Reviewed | en_US |
dc.contributor.affiliationum | Department of Mathematics, University of Michigan, 530 Church Street, Ann Arbor, MI, 48109, U.S.A. | en_US |
dc.contributor.affiliationumcampus | Ann Arbor | en_US |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/42571/1/10569_2005_Article_5437.pdf | en_US |
dc.identifier.doi | http://dx.doi.org/10.1007/s10569-005-5437-2 | en_US |
dc.identifier.source | Celestial Mechanics and Dynamical Astronomy | en_US |
dc.owningcollname | Interdisciplinary and Peer-Reviewed |
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