lecture1A_Jan7

Lecture1A_Jan7 - Overview of CDS 140B Introduction to Dynamics Wang Sang Koon Control and Dynamical Systems Caltech [email protected] Textbook

Info iconThis preview shows pages 1–12. Sign up to view the full content.

View Full Document Right Arrow Icon
Overview of CDS 140B: Introduction to Dynamics Wang Sang Koon Control and Dynamical Systems, Caltech [email protected]
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
± Textbook, Other Book and Papers I Textbook Stephen Wiggins [2003]: Introduction to Applied Nonlinear Dynamical Systems and Chaos , Second Edition. I Other Books and Paper Ferdinand Verhulst: Nonlinear Differential Equations and Dynamical Systems . Lawrence Perko: Differential Equations and Dynamical Systems . Koon, W.S., M.W. Lo, J.E. Marsden and S.D. Ross [2000]: Heteroclinic Connections between Periodic Orbits and Reso- nance Transitions in Celestial Mechanics, Chaos , 10, 427-469.
Background image of page 2
± Goals and Description of CDS 140B I A continuation of CDS 140A. 80% covers basic tools from nonlinear dynamics perturbation theory and method of averaging; bifurcation theory; global bifurcation and chaos; Hamiltonian systems. I Besides standard examples (van der Pol, Duffing, and Lorenz equations), 20% applies dynamical system tools in space mission design periodic and quasi-periodic orbits, invariant manifolds, homoclinic and heteroclinic connections, symbolic dynamics and chaos. I Examples: Genesis Discovery Mission and Low Energy Tour of Multiple Moons of Jupiter
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
± Outline of Presentation I Main Theme how to use dynamical systems theory of 3-body problem in space mission design. I Background and Motivation : NASA’s Genesis Discovery Mission. Jupiter Comets. I Planar Circular Restricted 3-Body Problem . I Major Results on Tube Dynamics . I Lobe Dynamics & Navigating in Phase Space. A Low Energy Tour of Jupiter’s Moons. I Conclusion and Ongoing Work . Two Full Body Problem and Astroid Pairs. Looking into Chemical Reaction Dynamics.
Background image of page 4
± Acknowledgement I H. Poincar´ e, J. Moser I C. Conley, R. McGehee, D. Appleyard I C. Sim´ o, J. Llibre, R. Martinez I G. G´ omez, J. Masdemont I B. Farquhar, D. Dunham I E. Belbruno, B. Marsden, J. Miller I K. Howell, B. Barden, R. Wilson I S. Wiggins, L. Wiesenfeld, C. Jaff´ e, T. Uzer I V. Rom-Kedar, F. Lekien, L. Vela-Arevalo I M. Dellnitz, O. Junge, and Paderborn group
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
± Genesis Discovery Mission I Genesis spacecraft is collecting solar wind samples from a L 1 halo orbit , will return them to Earth later this year for analysis. I Halo orbit , transfer / return trajectories in rotating frame. L 1 L 2 x (km) y(km) -1E+06 0 1E+06 -1E+06 -500000 0 500000 1E+06
Background image of page 6
± Genesis Discovery Mission
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
± Genesis Discovery Mission
Background image of page 8
± Genesis Discovery Mission I Follows natural dynamics, little propulsion after launch. I Return-to-Earth portion utilizes heteroclinic dynamics. L 1 L 2 x (km) y(km) -1E+06 0 1E+06 -1E+06 -500000 0 500000 1E+06
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
± Jupiter Comets
Background image of page 10
± Jupiter Comets I Rapid transition from outside to inside Jupiter’s orbit. I Captured temporarily by Jupiter during transition. I Exterior ( 2:3 resonance ). Interior ( 3:2 resonance ).
Background image of page 11

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 12
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 01/04/2012 for the course CDS 140b taught by Professor List during the Fall '10 term at Caltech.

Page1 / 45

Lecture1A_Jan7 - Overview of CDS 140B Introduction to Dynamics Wang Sang Koon Control and Dynamical Systems Caltech [email protected] Textbook

This preview shows document pages 1 - 12. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online