Untitled

Kotoulas, Thomas; Hadjidemetriou, John D.

doi:10.1023/a:1021321321221

Cited by 17 publications

(20 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For the EKB resonances, the planar circular problem has been extensively studied (Malhotra 1996;Kotoulas & Hadjidemetriou 2002;Voyatzis & Kotoulas 2005b). For all resonances (particularly of first, second and third order), the circular planar RTBP admits two families of symmetric periodic orbits called f amily I and f amily II which bifurcate from the family of circular orbits.…”

Section: Families Of 3d Orbits In the Circular Rtbpmentioning

confidence: 99%

See 1 more Smart Citation

Three dimensional periodic orbits in exterior mean motion resonances with Neptune

Kotoulas¹,

Voyatzis²

2005

A&A

View full text Add to dashboard Cite

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.

show abstract

Section: Families Of 3d Orbits In the Circular Rtbpmentioning

confidence: 99%

“…In Kotoulas & Hadjidemetriou (2002) the first order resonances 1/2, 2/3 and 3/4 were studied and the corresponding families of 3D periodic orbits were given. According to the classification introduced in Sect.…”

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

View full text Add to dashboard Cite

show abstract

“…The resonant families join smoothly the circular family, which shows a gap at the position of the first order resonance for µ = 0. A detailed study on the 1/2, 2/3 and 3/4 resonant families is given in Kotoulas and Hadjidemetriou (2002).…”

Section: Families Of Symmetric Periodic Orbits In the Planar Circularmentioning

confidence: 99%

“…We should remark that for e < 0.5 all resonances have stable families which are of symmetry type A. Additionally, the second and third order resonances have families of stable orbits of symmetry type B too. A detailed study for the resonant cases 1/2, 2/3 and 3/4 is given in Kotoulas and Hadjidemetriou (2002).…”

Section: Bifurcations From Planar Circular Rtbp To 3d Circular Rtbpmentioning

confidence: 99%

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

Kotoulas

Voyatzis

2004

Proc. IAU

Self Cite

View full text Add to dashboard Cite

Abstract. In the framework of the restricted three body problem, the resonant periodic orbits associated with the Kuiper belt dynamics are studied. Particularly, all the first, second and third order exterior mean motion resonances with Neptune located up to 50A.U. and the asymmetric resonances (beyond the 48 A.U.) are considered. We present the bifurcation points of families of periodic orbits of the planar circular problem from which families of periodic orbits are generated in the planar elliptic and in the 3D circular problem. Similarities and differences between the various resonant cases are noticed. The relation between the distribution of the bifurcation points and the population of small bodies at the particular resonances is discussed.

show abstract

“…Broucke (2001) made an extensive numerical study of orbits of planets of a binary star system in the three-dimensional restricted problem. A detailed analysis of symmetric periodic orbits of the 3D circular problem (CR3BP) at the exterior resonances 1:2, 2:3 and 3:4 was made by Kotoulas & Hadjidemetriou 2002. Basing our work on the latter paper, we proceed to the computation of the families of periodic orbits of the 3D elliptic restricted threebody problem (ER3BP).…”

Section: Introductionmentioning

confidence: 99%

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

Kotoulas¹

2005

A&A

View full text Add to dashboard Cite

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.

show abstract

Untitled

Cited by 17 publications

References 23 publications

Three dimensional periodic orbits in exterior mean motion resonances with Neptune

Three dimensional periodic orbits in exterior mean motion resonances with Neptune

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

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

Contact Info

Product

Resources

About