PHYS 5210

Fall 2022

Graduate Classical Mechanics

Course Information:

• Lectures: MWF 10:10-11 AM, University Club 13
• Syllabus, including general university policies

Lectures:

• Lecture 1 (August 22): Principle of least action
• Lecture 2 (August 24): Harmonic oscillation
• Lecture 3 (August 26): Relativistic motion
• Lecture 4 (August 29): Relativistic charged particles; Translation symmetry
• Lecture 5 (August 31): Noether's Theorem
• Lecture 6 (September 2): Boost symmetry; Configuration space
• Lecture 7 (September 7): Constraints and Lagrange multipliers
• Lecture 8 (September 9): Configuration space of rigid body rotation
• Lecture 9 (September 12): Euler's equations
• Lecture 10 (September 14): Euler angles
• Lecture 11 (September 16): The spinning top
• Lecture 12 (September 19): Vibrations of solids
• Lecture 13 (September 21): Lagrangian field theory and sound waves
• Lecture 14 (September 23): Noether's Theorem for fields
• Lecture 15 (September 26): The Klein-Gordon equation
• Lecture 16 (September 28): Relativistic electromagnetism
• Lecture 17 (September 30): Coupling electromagnetism to matter
• Lecture 18 (October 3): Effective field theory of a solid
• Lecture 19 (October 5): The elastic stress tensor
• Lecture 20 (October 7): Sound waves in solids
• Lecture 21 (October 10): Effective field theory of an ideal fluid
• Lecture 22 (October 12): Stress tensor of an ideal fluid
• Lecture 23 (October 14): Hamilton's equations
• Lecture 24 (October 17): Poisson brackets
• Lecture 25 (October 19): Symplectic manifolds and canonical transformations
• Lecture 26 (October 21): Generating functions of canonical transformations
• Lecture 27 (October 24): Noether's Theorem on symplectic manifolds
• Lecture 28 (October 26): The Hamilton-Jacobi equation
• Lecture 29 (October 28): Action-angle variables
• Lecture 30 (October 31): Integrable systems
• Lecture 31 (November 2): Perturbation theory: one degree of freedom
• Lecture 32 (November 4): Perturbation theory: many degrees of freedom
• Lecture 33 (November 7): The adiabatic theorem
• Lecture 34 (November 9): The Henon-Heiles Hamiltonian. Mathematica notebook.
• Lecture 35 (November 11): The kicked rotor. Mathematica notebook.
• Lecture 36 (November 14): The logistic map. Mathematica notebook.
• Lecture 37 (November 16): Linear stability analysis
• Lecture 38 (November 18): Renormalization group for period doubling
• Lecture 39 (November 28): Fractals
• Lecture 40 (November 30): Fractal structure of attractors. Mathematica notebook.
• Lecture 41 (December 2): The butterfly effect. Mathematica notebook.
• Lecture 42 (December 5): The KAM Theorem

Homework:

• Homework 1 (due August 29)
• Homework 2 (due September 7)
• Homework 3 (due September 12)
• Homework 4 (due September 19)
• Homework 5 (due September 26)
• Homework 6 (due October 3)
• Homework 7 (due October 10)
• Homework 8 (due October 17)
• Homework 9 (due October 24)
• Homework 10 (due October 31)
• Homework 11 (due November 7)
• Homework 12 (due November 14)
• Homework 13 (due December 5)

Exams:

• Practice Exam
• Exam (due December 12)