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

Jacques Henrard; Anne-Sophie Libert
September 2008
Celestial Mechanics & Dynamical Astronomy;Sep2008, Vol. 102 Issue 1-3, p177
Academic Journal
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.


Related Articles

  • Time stands still: devices and designs, allegory and alliteration, poetry and music and a new identification in an old portrait. Rooley, Anthony // Early Music;Aug2006, Vol. 34 Issue 3, p443 

    The article provides information on the devices and designs used in a portrait called the Old Hermit. It signifies confusions and struggles in life. It has been mentioned that some illustrations come in the form of a tent of white taffeta erected for various occasions with performing musicians...

  • Wagging Tongue. White, Cynthia // Stonewall County Courier (Aspermont, TX);9/27/2007, Vol. 21 Issue 48, p5 

    The article presents several weird trivia in the U.S. in 2007.

  • ALSO RECEIVED.  // Fortean Times;Jun2013, Vol. 302, p61 

    A bibliography on the subject of fortean phenomena is presented the books "Ninja Attack! True Tales of Assassins, Samurais and Outlaws," by Hiroko Yoda and Matt Alt, "Impossible Realities," by Maureen Caudill and "The Other Side of Truth," by Paul Kimball.

  • fast facts.  // Journal of Property Management;Mar/Apr2010, Vol. 75 Issue 2, p9 

    The article offers trivia which includes one about sheep's wool, about koala fingerprints, and another one about a shrimp's heart.

  • Are You Being Served? Bergwall, Hansa // Advocate;11/20/2007, Issue 997, p22 

    The article profiles gay men that are employed as personal assistants to the rich and famous. Several anecdotes of eccentric and exacting employers are presented, including a 60-year-old socialite who would become extremely angry if she ever saw a wrinkle in her clothing and younger socialite...

  • Born to be Mild. Westfalk, Mattias // Skin & Ink: The Tattoo Magazine;Apr2008, Issue 32, p52 

    The author shares his experiences with Sabado, a tattoo artist who started the Eccentric Super Tattoo shop in Nagoya, Japan with fellow tattoo artist Genko. He explains that he is filled with wonder when he sees more of Eccentric's work and it is with a sense of admiration when he hears Sabado...

  • ON SECOND THOUGHT. Rooney, Andy // Saturday Evening Post;Mar84, Vol. 256 Issue 2, p16 

    Reflects on minuscule matters, from barking dogs that bite to asking pardon when knocked down. Use of revolving doors; Growth rate of the average American; Arguments that arise at civic meetings; Importance of punctuality; Farmers' ownership of large, expensive equipment that they rarely use.

  • Ski-joring, Bob Snorkeling and Cow Pies. Cook, Kevin; O'Brien, Richard // Sports Illustrated;01/11/99, Vol. 90 Issue 1, p30 

    Discusses some strange sports events of 1999. The Shovetide Pancake Race; Ski-Joring Finals; Shamrock Sportsfest; Typewriter Toss; World Championships of Toe Wrestling; World Bog Snokeling Championships; Others.

  • 22. MISS VINT AND HER REINCARNATED CATS. BONDESON, JAN // Fortean Times;Jun2013, Vol. 302, p78 

    The article discusses the story in the October 1892 issue of "Illustrated Police News" about the spinster Miss Vint and her cats. It explains that Miss Vint found a kitten on her doorstep and decided to keep it as part of her household because of the kitten's striking resemblance to his deceased...


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics