gab_caltech03

gab_caltech03 - Restricted four and five body problems in...

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Unformatted text preview: Restricted four and five body problems in the Solar System Frederic Gabern and ` Angel Jorba CDS Seminar. October 8, 2003. Frederic Gabern Applied Mathematics and Analysis Control and Dynamical Systems University of Barcelona California Institute of Technology 1 Contents Introduction. The Trojan asteroids. Review of the existing results. Motivation for the present work. Periodic models. The Bicircular Coherent Problem. The Elliptic Restricted Three Body Problem. Quasi-periodic models. The Bianular Problem. The Tricircular Coherent Problem. Conclusions. 2 The Trojan asteroids (I) Sun Jupiter 60 60 L5: Trojan asteroids L4: Greek asteroids L 4 : L 5 : Achilles Patroclus Hector Aeneas Nestor Memnon Agamemnon Paris 3 The Trojan asteroids (II) 4 The Trojan asteroids (III) 5 Previous Work The Restricted Three Body Problem Analytic Tools. Semi-analytic tools. Theoretical Results m The Outer Solar System Frequency analysis. Lyapunov exponents. Numerical Results 6 The Restricted Three Body Problem The dynamics around the triangular points of the Sun-Jupiter system has been studied using analytical and semi-analytical tools (transformation of the Hamiltonian to a normal form , computation of some approximate first integrals ) by several authors: Giorgilli, Delshams, Fontich, Galgani & Simo , 1989; Simo , 1989; Celletti & Giorgilli , 1991; Jorba & Simo , 1994 (in the elliptic case); Giorgilli & Skokos , 1997; Skokos & Dokoumetzidis , 2000. 7 Realistic Model: OSS The dynamics of some jovian Trojan asteroids has been studied in several papers using the Outer Solar System : Bien & Schubart , 1987; Milani , 1993; Levison, Shoemaker & Shoemaker , 1997; Pilat-Lohinger, Dvorak & Burger , 1999; Tsiganis, Dvorak & Pilat-Lohinger , 2000. 8 Some New Models We want to build and study models more sophisticated than the RTBP. These models will try to simulate in a better way the relative Sun-Jupiter motion and they will be written as a RTBP perturbation in order the semi-analytical tools can be applied. In this work, we focus on the following models: The Bicircular Coherent Problem ( BCCP ). The Elliptic Restricted Three Body Problem ( ERTBP ). The Bianular Problem ( BAP ). The Tricircular Coherent Problem ( TCCP ). 9 The BCCP Model (I) We look for a periodic solution of the planar Sun-Jupiter-Saturn Three Body Problem . The period is chosen to be the relative period of Saturn in the Sun-Jupiter RTBP system: T sat . The osculating eccentricity of Jupiter is small (about 50 times smaller than the real one) but the semi-major axis and the period are quite well adjusted to the actual ones....
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This note was uploaded on 01/04/2012 for the course CDS 280 taught by Professor Marsden,j during the Fall '08 term at Caltech.

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gab_caltech03 - Restricted four and five body problems in...

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