NDLI: Periodic orbits as centers of stability in the secular 3D planetary three body problem

Content Provider	Springer Nature Link
Author	Henrard, Jacques Libert, Anne Sophie
Copyright Year	2008
Abstract	In a previous paper, we have developed an analytical model of the secular 3D planetary problem by expanding the perturbation function up to the twelfth order in the eccentricities and the inclinations. Although the expansion is limited the model is able to describe with accuracy most of the observed systems of exoplanets. With the help of this model we were able to describe the geometry of the phase space of a typical system. The kernel of this description is a series of surfaces of section showing the chaotic and the regular domains of the phase space. We have observed in this previous paper that a family of unstable periodic orbits is responsible for the chaoticity, while we have hinted that the islands of stability are organized around stable periodic orbits. In this contribution we compute the main families of periodic orbits of the problem and show that indeed they are responsible for sculpting the phase space.
Starting Page	177
Ending Page	189
Page Count	13
File Format	PDF
ISSN	09232958
Journal	Celestial Mechanics and Dynamical Astronomy
Volume Number	102
Issue Number	1-3
e-ISSN	15729478
Language	English
Publisher	Springer Netherlands
Publisher Date	2008-02-12
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Exoplanetary systems Three body problem Periodic orbits Homoclinic orbits Stability Bifurcations Mathematics Astronomy
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Mathematical Physics Astronomy and Astrophysics Modeling and Simulation Computational Mathematics Space and Planetary Science

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Numerical Determination of Homoclinic and Heteroclinic Orbits at Collinear Equilibria in the Restricted Three-Body Problem with Oblateness

The manifolds of families of 3D periodic orbits associated to Sitnikov motions in the restricted three-body problem

Periodic orbits and bifurcations in the Sitnikov four-body problem

Families of Periodic Orbits Emanating From Homoclinic Orbits in the Restricted Problem of Three Bodies

Analytical Approach to the Secular Behaviour of Exoplanetary Systems

Periodic Orbits of a Collinear Restricted Three-Body Problem

Secular frequencies of 3-D exoplanetary systems

Global Bifurcations of Periodic Solutions of the Restricted Three Body Problem

2/1 resonant periodic orbits in three dimensional planetary systems

Periodic orbits as centers of stability in the secular 3D planetary three body problem

Similar Documents

Numerical Determination of Homoclinic and Heteroclinic Orbits at Collinear Equilibria in the Restricted Three-Body Problem with Oblateness

The manifolds of families of 3D periodic orbits associated to Sitnikov motions in the restricted three-body problem

Periodic orbits and bifurcations in the Sitnikov four-body problem

Families of Periodic Orbits Emanating From Homoclinic Orbits in the Restricted Problem of Three Bodies

Analytical Approach to the Secular Behaviour of Exoplanetary Systems

Periodic Orbits of a Collinear Restricted Three-Body Problem

Secular frequencies of 3-D exoplanetary systems

Global Bifurcations of Periodic Solutions of the Restricted Three Body Problem

2/1 resonant periodic orbits in three dimensional planetary systems

Periodic orbits as centers of stability in the secular 3D planetary three body problem