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HU Credits:
3
Degree/Cycle:
2nd degree (Master)
Responsible Department:
Physics
Semester:
2nd Semester
Teaching Languages:
English and Hebrew
Campus:
E. Safra
Course/Module Coordinator:
Dr. Ido Barth
Coordinator Office Hours:
By appointment
Teaching Staff:
Dr. Ido Barth
Course/Module description:
Advanced course in analytical mechanics
Course/Module aims:
1. To deepen the theoretical understanding of nonlinear multidimensional Hamiltonian systems.
2. To provide applicable knowledge in perturbation theories and in numerical methods for dynamical systems.
Learning outcomes - On successful completion of this module, students should be able to:
1. To analyze Hamilonian systems by the means of action-angle variables.
2. To identify symmetries, topology, constants of motion, and adiabatic invariants.
3. To use perturbation theories for solving stationary, dynamical, and resonant problems.
4. To write a symplectic scheme for numerical simulations of dynamical systems.
Attendance requirements(%):
0
Teaching arrangement and method of instruction:
Lecture, exercise, and homework
Course/Module Content:
1. A review of the formalisms of Lagrange, Hamilton, and Hamilton-Jacobi.
2. The Symplectic condition for canonical transformations, Poisson brackets, phase space, Liouville theorem, infinitesimal canonical transformations, and Symplectic numerical schemes.
3. The variational principle, the abbreviated action, and the action integral.
4. Action-angle variables, integrability, phase space topology, degeneracy, and Poincare surface of section. Examples: the Harmonic oscillator, the anharmonic oscillator (pendulum), the Kepler problem.
5. Perturbation theories: Time independent perturbation theory, nearly integrable systems Canonical perturbation theory, secular (time dependent) perturbation theory, nonlinear resonance, Chirikov criterion for resonance overlap, Arnold diffusion, KAM theorem,
6. Adiabatic invariants.
7. Autoresonance.
8. Introduction to classical field theory.
Required Reading:
non
Additional Reading Material:
• H. Goldstein, Classical mechanics, (Pearson 2013).
• L.D. Landau and E.M. Lifshitz, Mechanics, (Addison–Wesley 1960).
• A.J. Lichtenberg and M.A. Lieberman, Regular and stochastic motion, (Springer 1983).
• R.Z. Sagdeev, D.A. Usikov, and G.M. Zaslavsky, Nonlinear physics - from the pendulum to turbulence and chaos, (Harwood 1988).
Grading Scheme :
Essay / Project / Final Assignment / Referat 30 %
Submission assignments during the semester: Exercises / Essays / Audits / Reports / Forum / Simulation / others 70 %
Additional information:
none
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