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Introduction to Hamiltonian Dynamics, Spring 2017
Teacher: Paolo Muratore-Ginanneschi
Scope: 7 cr
Type: Advanced
Teaching:
Topics: Classical Mechanics, Lagrange and Hamiltonian formalism, Chaos in Nonlinear Hamiltonian Dynamics.
Prerequisites:
News
Teaching schedule
16.1.-14.5.2017, Tue from 10-12, room C122. Exercise group Thu 10-12, room C122.
Exams
Exam lasts 2,5 hours.
You can use (lecturer will fill in) in the exam.
Course material
The course will draw mostly from the following references.
Wimberger S., Nonlinear Dynamics and Quantum Chaos, Springer Graduate Texts in Physics (2014).
Arnol'd, V. I., Mathematical methods of classical mechanics, Springer-Verlag 2nd edition (1989).
- Ozorio de Almeida, A. M., Hamiltonian systems : Chaos and quantization, Cambridge University Press (1988).
- Strogatz, S.H.: Nonlinear Dynamics and Chaos with Applications to Physics, Biology, Chemistry and Engineering, Westview Press Classroom Classics (2014).
- Scheck, F.: Mechanics: From Newton's Laws to Deterministic Chaos , Springer-Verlag Berlin Heidelberg, (2010).
Course contents
Lecture 01: Examples of elementary dynamical systems | Lecture 09: Lagrangean variational principles (14.03) |
| Lecture 02: Existence and uniqueness theorems for ODE’s (01.02) | Lecture 10: Hamiltonian variational principle |
| Lecture 03: Hamiltonian vector fields and time reversal (08.02) | Lecture 11: Noether's first and second theorem |
| Lecture 04: Linear systems, Hartman-Grobman theorem (08.02) | Lecture 12: Equivariance and Poisson brackets |
| Lecture 05: Linear autonomous Hamiltonian systems (11.02) | Lecture 13: Canonical transformations |
| Lecture 06: Linear periodic systems and stability of periodic orbits | Lecture 14: Hamilton--Jacobi and dynamic programming |
| Lecture 07: Poincaré section, periodic orbits and Poincaré recurrence (02.03) | Lecture 15: Liouville Arnold integrable systems |
| Lecture 08: D'Alembert principle and Euler–Lagrange equations (04.03) | Lecture 16: Birkhoff integrable systems |
Lecture notes available from the latest installment of this course.
Registration
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Exercises
Assignments
- Exercise set 1 (09.02)
- Exercise set 2 (14.02)
- Exercise set 3 (27.02)
- Exercise set 4 (01.03)
- Exercise set 5 (14.03)
- Exercise set 6 (29.03: one typo corrected in assignment 1)
- Exercise set 7
- Exercise set 8
- Exercise set 9
Exercise classes
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Course feedback
Course feedback can be given at any point during the course. Click here.