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Physics 515: "Classical Dynamics"

 

Course Outline


 

INSTRUCTOR:

Prof. Edison Liang, HBH Room 342, liang@rice.edu

TIME:

Tu Th 9:25-10:40AM

ROOM:

Bonner Conference Room, HBH 223

 

TEXT:

Fetter and Walecka, Theoretical Mechanics of Particles and Continua, Dover Paperback (2003 or latest edition)

 

OTHER  REFERENCES:  

Fetter and Walecka, Nonlinear Mechanics: A Supplement to Theoretical Mechanics of Particles and Continua

Goldstein, Classical Mechanics

 Landau and Lifshitz, Mechanics

Marion, Classical Dynamics of Particles and Systems

Mathews  & Walker, Mathematical Methods of Physics

 

HOMEWORK:

 ~ 2 problems every week

 

GRADER:

Yaxue Dong

 

GRADES:

65% Homework, 10% Mid-Term, 25% Final

 

WEBSITE:    spacibm.rice.edu/~liang/phys515

 

Tentative No. Of Lectures

Topics

Text Chapter #

3

Laws of Motion and Conservation Laws, Inertial Frames, Noninertial and Rotating Frames, Galilean Transformation, Generalized Transformations, Tensor Notations

1, 2

4

Variational Principle and Lagrangian Dynamics: Constraints and Lagrange Multipliers, Hamiltonian, Symmetry and Constants of Motion, Similarity

3

2

Brief Review of Central Forces, Kepler’s Problem, Scattering

1

2

Small Oscillations: Normal Modes and Eigenvalue Problems, Driven Oscillations and Resonance, Dissipation, Anharmonic Oscillations

4

2

Brief Review of Rigid Body Motions: Euler Angles, Euler Equations of Motion

5

4

Hamiltonian Dynamics:  Canonical Transformations, Action-Angle Variable, Hamilton-Jacobi Theory; Poisson Brackets, Transition to Quantum Mechanics, Symmetry Principles and Contact Transformations, Liouville’s Theorem

6

3

Nonlinear Dynamics and Chaos

supplement

3

Strings and Membranes: Waves, Sturm-Liouville Equations, Green Function, Perturbation Theory WKB Approximation, Boundary Value Problems

7, 8

4

Introduction to Fluid Mechanics, Sound Waves and Acoustics, Shock Waves, Dispersion and Nonlinearity

9, 10

 

Examples of Math Topics covered in this course:

  1. Non-Cartesian coordinates & vector calculus.
  2. Complex variables including contour integration.
  3. Delta-function and distributions.
  4. Ordinary differential equations:  eigenfunction expansions and boundary value problems.
  5. Sturm-Lioville systems and special functions.
  6. Matrices, tensors, eigenvectors and eigenvalues.
  7. Linear partial differential equations and Green function techniques.
  8. Variational methods.
  9. Perturbation theory.