Periodic Orbits of the Planetary Type and their Stability

Hadjidemetriou, John D.

doi:10.1007/978-94-009-2285-3_32

Cited by 4 publications

(2 citation statements)

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“…1b). The stability of periodic orbits has been studied many times in the past (Hénon 1965;Hadjidemetriou 1988;Celletti et al 2002). The transition from stability to instability and vice versa in the family II 1:2 coincides with the bifurcation to asymmetric librations.…”

Section: The Circular Casementioning

confidence: 99%

“…A detailed analysis of families of periodic orbits in the planar circular restricted problem and their stability was performed by Hadjidemetriou & Ichtiaroglou (1984) for µ = 0.001. Moreover, a review of different types of periodic orbits is given in Hadjidemetriou (1988). An atlas of the planar circular restricted three-body problem was produced by Winter & Murray (1994a,b).…”

Section: Introductionmentioning

confidence: 99%

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The dynamics of the 1:2 resonant motion with Neptune in the 3D elliptic restricted three-body problem

Kotoulas¹

2005

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Abstract. We study the planar and the three-dimensional 1:2 resonant motion with Neptune (N1:2) in the framework of the elliptic restricted three-body problem. We examine the dynamics at the 1:2 mean motion resonance with Neptune in a hierarchy of models: the planar circular, the planar elliptic, the three-dimensional circular and the three-dimensional elliptic restricted three body problem. We start from the planar circular model in which we compute families of symmetric periodic orbits with stable and unstable segments. Using the circular planar model as the basic model, we proceed to more realistic models, namely the planar elliptic and the 3D circular problem. Families of symmetric periodic orbits of the above models bifurcate from the families of periodic orbits of the planar circular problem. Moreover, we compute families of symmetric periodic orbits in the 3D elliptic restricted three-body problem. These new families bifurcate from the families of periodic orbits of the planar elliptic and the 3D circular problem. The stability of all orbits is studied and the structure of the phase space is discussed in detail.

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Section: The Circular Casementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%