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CDS 140b: Course Lectures
CDS 140b - Introduction to Dynamics
COURSE LECTURES AND OUTLINE
Second Term: Winter 2004
Instructor:
Wang Sang Koon
Course Lectures: highlighted/underlined materials are in pdf format.
- Week 1: Read [Verhulst] sections 9.1-9.4, and 10.1-10.2.
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Week 2: Read [Verhulst] sections 10.3-10.4 ( and [Perko] section 3.5, optional).
- lecture 2A
The Poincare-Lindstedt method and the computation of periodic orbits.
- lecture 2B Application to space mission design: the computation of a halo orbit and its invariant manifolds.
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Week 3: Read [Verhulst] 11.1-11.5, and 11.8.
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Week 4: Read [Wiggins] chapter 18 and section 19.1.
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Week 5: Read [Wiggins] section 19.2 and sections 20.1-20.2.
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Normal forms.
- lecture 5B Final project introduction
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Week 6: Read [Wiggins] chapters 23 and 24.
- Bifurcation of equilibrium solutions and Hopf bifurcation.
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Introduction to chaos: symbolic dynamics, Smale horseshoe, Conley-Moser conditions, and homoclinic and heteroclinic dynamics.
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Week 7: Read [Wiggins] chapters 25 and 26.
- Introduction to Melnikov method.
- The chaotic dynamics in the restricted three-body problem and its application to mission design.
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Week 8: Read [Verhulst] sections 15.1-15.4.
- Introduction to Hamiltonian systems.
- Birkhoff normalization. The phenomenon of recurrence.
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Week 9: Read [Verhulst] sections 15.5-15.8.
- Periodic solutions. Invariant tori and chaos. The KAM theorem.
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Week 10: Introduction to chaotic transport theory. Its application in dynamical astronomy, space mission design, and fluid mechanics.
CDS 140b
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