CDS 241: Geometric Mechanics

1997-1998

(Offered alternate years)

Course Description:

The geometry and dynamics of Lagrangian and Hamiltonian systems, including sympl ectic and Poisson manifolds, variational principles, Lie groups, momentum maps, rigid- body dynamics, Euler-Poincar\002 equations, stability, and an introduction to reduction theory. More advanced topics will include reduction theory, fluid dynamics, the energy momentum method, geometric phases, bifurcation theory for mechanical systems, and nonholonomic systems.

Second Term: Winter 1998

Time and Place: 125 Steele; M 1:00-2:30 p.m. with alternative 4:00-5:30 p.m.; W 4:00-5:30 p.m.

Instructor: Jerrold Marsden, marsden@cds.caltech.edu; Office Hours: M 3:00-4:00 p.m., T 2:00-3:00 p.m, 119 Steele
Teaching Assistant: Antonio Hernandez, antonio@cco.caltech.edu
Office Hours: Thursdays: 4 - 5.30 pm, room 110, Steele.
Tuesdays: same place, 6.30 - 7.30 pm, (by email appointment only)

Course Syllabus

Copies of the new edition of "Mechanics and Symmetry" will be made available. The goal is to get through as much of the book as we can for the Winter term.
Homework will be assigned weekly and there will be a midterm and a final.

Chapter 1: Introduction (pdf)
Chapter 2: Hamiltonian Systems on Linear Symplectic Spaces (pdf)
Chapter 3: Introduction to Infinite Dimensional Systems (pdf)
Chapter 4: Manifolds and Differential forms (Review) (pdf)
Chapter 5: Hamiltonian Systems on Symplectic Manifolds (pdf)
Chapter 6: Cotangent Bundles (pdf)
Chapter 7: Lagrangian Mechanics (pdf)
Chapter 8: Variational Principles (pdf)
Chapter 9: Lie Groups (pdf)
Chapter 10: Poisson Manifolds (pdf)
Chapter 11: Momentum Maps (pdf)
Chapter 12: Computation of Momentum Maps (pdf)
Chapter 13: Euler-Poincare and Lie-Poisson Reduction (pdf)
Chapter 14: Coadjoint Orbits (pdf)
Chapter 15: The Rigid Body (pdf)
References: (pdf) Part II

Homework Assignments