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HU Credits:
3
Degree/Cycle:
2nd degree (Master)
Responsible Department:
Physics
Semester:
2nd Semester
Teaching Languages:
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. Dynamics in phase space, Liouville theorem, and Poisson brackets.
3. The variational principle, canonical transformations, action-angle variables, adiabatic invariants, and phase space topology.
4. Integrability, Symmetry, and constants of motion.
5. Canonical perturbation theory, time dependent perturbation theory, averaging methods.
6. Nonlinear oscillator, nonlinear resonance, autoresonance, three wave interaction, and parametric resonance.
7. Chirikov resonance-overlap criterion, Arnold diffusion, nearly integrable systems, KAM theorem, Poincare map, Stochasticity, and chaos.
8. Symplectic schemes for numerical simulations of dynamical systems.
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).
Course/Module evaluation:
End of year written/oral examination 0 %
Presentation 0 %
Participation in Tutorials 0 %
Project work 100 %
Assignments 0 %
Reports 0 %
Research project 0 %
Quizzes 0 %
Other 0 %
Additional information:
non
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