Linear Stability Analysis of Resonant Periodic Motions in the Restricted Three-Body Problem
dc.contributor.author | Viswanath, Divakar | en_US |
dc.date.accessioned | 2006-09-11T15:22:36Z | |
dc.date.available | 2006-09-11T15:22:36Z | |
dc.date.issued | 2005-04 | en_US |
dc.identifier.citation | Viswanath, D.; (2005). "Linear Stability Analysis of Resonant Periodic Motions in the Restricted Three-Body Problem." Journal of Dynamics and Differential Equations 17(2): 271-292. <http://hdl.handle.net/2027.42/44865> | en_US |
dc.identifier.issn | 1040-7294 | en_US |
dc.identifier.issn | 1572-9222 | en_US |
dc.identifier.uri | https://hdl.handle.net/2027.42/44865 | |
dc.description.abstract | The equations of the restricted three-body problem describe the motion of a massless particle under the influence of two primaries of masses 1 −μ and μ, 0≤μ≤ 1/2, that circle each other with period equal to 2π. When μ=0, the problem admits orbits for the massless particle that are ellipses of eccentricity e with the primary of mass 1 located at one of the focii. If the period is a rational multiple of 2π, denoted 2π p / q , some of these orbits perturb to periodic motions for μ > 0. For typical values of e and p / q , two resonant periodic motions are obtained for μ > 0. We show that the characteristic multipliers of both these motions are given by expressions of the form in the limit μ→ 0. The coefficient C ( e , p , q ) is analytic in e at e =0 and C ( e , p , q )= O ( e | p - q | ). The coefficients in front of e | p - q | , obtained when C ( e , p , q ) is expanded in powers of e for the two resonant periodic motions, sum to zero. Typically, if one of the two resonant periodic motions is of elliptic type the other is of hyperbolic type. We give similar results for retrograde periodic motions and discuss periodic motions that nearly collide with the primary of mass 1 −μ. | en_US |
dc.format.extent | 195753 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-Plenum Publishers; Springer Science+Business Media, Inc. | en_US |
dc.subject.other | Mathematics | en_US |
dc.subject.other | Collision Orbits | en_US |
dc.subject.other | Three-body Problem | en_US |
dc.subject.other | Ordinary Differential Equations | en_US |
dc.subject.other | Partial Differential Equations | en_US |
dc.subject.other | Applications of Mathematics | en_US |
dc.subject.other | Resonance | en_US |
dc.subject.other | Action-angle Variables. | en_US |
dc.title | Linear Stability Analysis of Resonant Periodic Motions in the Restricted Three-Body Problem | en_US |
dc.type | Article | en_US |
dc.subject.hlbsecondlevel | Mathematics | 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, USA | en_US |
dc.contributor.affiliationumcampus | Ann Arbor | en_US |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/44865/1/10884_2005_Article_5406.pdf | en_US |
dc.identifier.doi | http://dx.doi.org/10.1007/s10884-005-5406-1 | en_US |
dc.identifier.source | Journal of Dynamics and Differential Equations | en_US |
dc.owningcollname | Interdisciplinary and Peer-Reviewed |
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