Generating Families in the Restricted Three-Body Problem

II. Quantitative Study of Bifurcations
Softcover Nachdruck of the original 1. Auflage 2001
ISBN: 978-3-662-14517-3
Verlag: Springer

Buch, Englisch, Band 65, 304 Seiten, Paperback, Format (B × H): 155 mm x 235 mm, Gewicht: 487 g

Reihe: Lecture Notes in Physics Monographs

hereafter calledvolume the of In a volume study previous (H6non 1997, I), the restricted initiated. families in problem (We generating three body was recallthat families defined asthe limits offamilies of are periodic generating determinationof orbitsfor Themain wasfoundto lieinthe 4 problem p 0.) bifurcation wheretwo the betweenthebranches ata ormore orbit, junctions A solutionto this was familiesof orbits intersect. partial problem generating and sidesof theuseofinvariants: Manysimple symmetries passage. givenby In the evolution of the bifurcations can be solved in this way. particular, orbits be described almost nine natural families of can completely. periodic become i.e.when thenumber of asthe bifurcations morecomplex, However, fails. the bifurcation orbit themethod families increases, passingthrough of This volume describes another to the a approach problem, consisting in of bifurcation ofthe families the a analysis vicinity detailed, quantitative used in Vol. I. orbit. This moreworkthan the requires qualitativeapproach in at to deter it has the of least, However, advantage allowing us, principle branches Infact it morethanthat: minein allcaseshowthe are joined. gives almost all the first order we will see in asymptotic approxima that, cases, the families in the ofthe bifurcation can be derived. tion of neighbourhood found in with This a comparison numerically allows, particular, quantitative families. and The 11 dealswiththerelevant definitions Chapter generalequations. of describedin 12 16.The ofbifurcations 1 is Chaps. study type quantitative it is described in 17 23. 3 of 2 ismore Chaps. Type analysis type involved; its hadnot been at thetime of isevenmore completed complex; analysis yet writing.

Zielgruppe

Research

Autoren/Hrsg.

Henon, Michel

Fachgebiete

• Naturwissenschaften Astronomie Astrophysik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Naturwissenschaften Astronomie Raumfahrt
• Naturwissenschaften Physik Angewandte Physik Astrophysik
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik

Inhaltsverzeichnis

Definitions and General Equations.- Quantitative Study of Type 1.- Partial Bifurcation of Type 1.- Total Bifurcation of Type 1.- The Newton Approach.- Proving General Results.- Quantitative Study of Type 2.- The Case 1/3 v < 1/2.- Partial Transition 2.1.- Total Transition 2.1.- Partial Transition 2.2.- Total Transition 2.2.- Bifurcations 2T1 and 2P1.