Bifurcations of periodic orbits and potential stability regions in Kuiper belt dynamics

Kotoulas, Thomas; Voyatzis, George

doi:10.1017/s1743921304008853

Cited by 2 publications

(3 citation statements)

References 5 publications

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“…The bifurcation points of families of 3D periodic orbits are given in Kotoulas and Voyatzis (2004b). The 3D resonant structure should provide useful information about the capture of trans-Neptunian objects in highly inclined orbits.…”

Section: Discussionmentioning

confidence: 99%

“…Namely, starting from a generating orbit at e ′ = 0, a family of periodic orbits of constant period is formed by varying e ′ (the parameter of the family). In Table 1 we present the values of eccentricity and Jacobi constant that correspond to the bifurcation points found in the studied resonances (see also Kotoulas and Voyatzis, 2004b). From each BPl two families bifurcate, denoted as E p/q lp or E p/q la , where p/q is the resonance, l is the bifurcation point (according to the numbering in the first row of Table 1, which is based on the ascending sorting of the corresponding eccentricity values) and the second subscript p or a denotes the initial position of Neptune is at perihelion or aphelion respectively.…”

Section: The Elliptic Restricted Three-body Problemmentioning

confidence: 99%

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Planar periodic orbits in exterior resonances with Neptune

Voyatzis

Kotoulas

2005

Planetary and Space Science

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In the framework of the planar restricted three body problem we study a considerable number of resonances associated to the Kuiper Belt dynamics and located between 30 and 48 a.u. Our study is based on the computation of resonant periodic orbits and their stability. Stable periodic orbits are surrounded by regular librations in phase space and in such domains the capture of trans-Neptunian object is possible. All the periodic orbits found are symmetric and there is evidence for the existence of asymmetric ones only in few cases. In the present work first, second and third order resonances are under consideration. In the planar circular case we found that most of the periodic orbits are stable. The families of periodic orbits are temporarily interrupted by collisions but they continue up to relatively large values of the Jacobi constant and highly eccentric regular motion exists for all cases. In the elliptic problem and for a particular eccentricity value of the primary bodies the periodic orbits are isolated. The corresponding families, where they belong to, bifurcate from specific periodic orbits of the circular problem and seem to continue up to the rectilinear problem. Both stable and unstable orbits are obtained for each case. In the elliptic problem the unstable orbits found are associated with narrow chaotic domains in phase space. The evolution of the orbits, which are located in such chaotic domains, seems to be practically regular and bounded for long time intervals.

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Section: Discussionmentioning

confidence: 99%

Section: The Elliptic Restricted Three-body Problemmentioning

confidence: 99%

Planar periodic orbits in exterior resonances with Neptune

Voyatzis

Kotoulas

2005

Planetary and Space Science

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“…In family I the small body is at perihelion at t = 0, while in family II the small body is at aphelion at t = 0 (for more details, see Voyatzis & Kotoulas 2005b). In Kotoulas & Voyatzis (2005a) The family of circular orbits C in the planar case is not continued near the first order resonances for µ > 0. So, it is not expected to have 3D circular periodic orbits in this case.…”

Section: Families Of 3d Orbits In the Circular Rtbpmentioning

confidence: 99%

Three dimensional periodic orbits in exterior mean motion resonances with Neptune

Kotoulas¹,

Voyatzis²

2005

A&A

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Abstract. In the framework of the three dimensional restricted three-body problem we study the dynamics of the exterior mean motion resonances with Neptune. The basis of our study is the computation of periodic orbits and their linear stability. The position and stability of periodic orbits critically determine the phase space topology. Stable periodic orbits are centers of regular librations where resonant trapping of minor bodies can take place. The periodic orbits are continued analytically from the planar model to the three-dimensional one forming families, which, in most cases, extend up to high inclination values and pass to the regime of retrograde motion. A classification of the families, according to their continuation and termination, is given. The computations show that resonant librating motion is present up to high inclination values and for particular eccentricity domains. When the ellipticity of the Neptune's orbit is taken into account, periodic orbits are found only for very high inclination values and all of them are unstable.

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Bifurcations of periodic orbits and potential stability regions in Kuiper belt dynamics

Cited by 2 publications

References 5 publications

Planar periodic orbits in exterior resonances with Neptune

Planar periodic orbits in exterior resonances with Neptune

Three dimensional periodic orbits in exterior mean motion resonances with Neptune

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