Faculty Supervisor:
Dr. Mona Berciu
Course Coordinators:
Ryan McKenzie
Jordan Schultz
Meetings: Wed. 3-5pm, Hebb 12. Course Outline: Review of Lagrangian Dynamics, principle of least action, Hamiltonian dynamics, Hamilton's canonical equations, first integrals, Hamilton-Jacobi theory, Poisson brackets, Liouville's theorem, Noether's theorem, action angle variables. If time permits, applications to chaotic dynamics, continuous systems and fields and the path-integral link to quantum mechanics will be investigated. Course Description: This is a student directed, seminar style course and as such the topics to be covered are flexible. Students will study on their own the reading material and meet weekly to discuss their progress. In the last three weeks of the course, students will work on individual projects of their choice. The project counts as 40% of the final grade, the other 60% are from assignments. References: G : Goldstein, Poole and Safko, Classical mechanics, 3rd edition. LL : Landau and Lifshitz, Mechanics - course of theoretical physics, vol. 1, 3rd edition. P : Percival and Richards, Introduction to dynamics. HF : Hand and Finch, Analytical mechanics.Reading material and assignments: (will be updated weekly)
| When | What | From where | Homework |
| week 1 | review of lagrangian mechanics | G: 1.4-1.6, 2.1-2.4 (or LL: 1,2,4,5) |
Assignment 1 |
| week 2 | Hamiltonian formalism | G: 8.1; HF: 5.3-5.5; P: 5.1-5.4 | Assignment 2 |
| week 3 | Conservation laws, first integrals Liouvilles's theorem |
P: entire chap. 4; HF: 5.1, 5.2; G: 8.2 |
PR: chap. 4, problems 3,5,8,13,17. |
| week 4 | Canonical transformations | P: entire chap. 6; | PR: chap. 6, problems 2,4,9,13,15. |
| week 5 | Poisson brackets; Hamilton-Jacobi equation | HF: 6.3,6.4; | HF: chap. 6, problems 8, 12a, 15, 16, 17. |
| week 6 | Action-angle variables | P: entire chap. 7 | P: chap. 7, problems 2, 5, 6, 7, 11a. |
| week 7 | Reading week | ||
| weeks 8,9 | choosing project topics | working on individual projects | |
| weeks 10, 11 | Chaotic dynamics | HF: entire chap. 11 | working on individual projects |
| week 12 | Formulations for continuous fields | G: chap. 12-1, 12-2, 12-3, 12-4 | 1, 4 and 10 |
| week 13 | Path integrals in quantum mechanics | handnotes from Mona | none |
Projects: Jordan: HF #4 (Lorenz equations) Ryan M: The Henon-Heiles Hamiltonian Karla: The restricted three-body problem Ryan S: Asteroids Alex : Entrainment; Fireflies demo1, demo2. Gretchen: Diffusion Limited Aggregation Dan: Wilberforce Pendulum Derek: Chaos dynamics and the logistic map Names in Hamiltonian Dynamics: