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Physics 507, Fall 2010


This is a tentative schedule of what we will cover in the course. It is subject to change, often without advance notice. These will occur in response to the speed with which we cover material, individual class interests, and possible changes in the topics covered.

  Date Topic Pages
L1 9/2 Particle Dynamics; \vec F ,T, W, \tau,U(\vec r); P, L; cm; 1-8
L2 9/8 Systems of particles; Constraints, Generalized coordinates; Mass Matrix; Phase Space; Dynamical Systems; 8-20
H1 9/9 Homework Assignment # 1 (1.1, 1.2)
L3 9/9 phase curves and flows; fixed points, invariant sets; stablility; Types of fixed points; seperatrix; Lagrangian 20-36
L4 9/13 Constraints; D'Alembert; Lagrange's equations; Hamilton's Principle and Action 36-44
H2 9/16 Homework Assignment # 2 (1.4, ~1.5 )
L5 9/16 Variational calculus; Ignorable coords, conserved quantities; Hamilton's Equations; Velocity-dependent forces. 45-53
L6 9/20 2-body central forces; Kepler problem; a, e, L, E, T 54-67
L7 9/23 Nearly circular orbits; closed orbits; Runge-Lenz;Virial Theorem 67-73
H3 9/23 Homework Assignment # 3 to view to print
L8 9/27 Rutherford scattering; Rainbow, glory. Config space for rigid body 74-80
L9 9/30 Groups Rotating kinematics, \vec \omega, Coriolus 83-95
H4 9/30 Homework Assignment # 4
L10 10/4 inertia tensor; L, T of cm and about cm. \parallel and \perp axis theorems; Principal Axes; tire balancing 95-104
L11 10/7 Euler's equations. Axisymmetric free body; General free rigid body; Poinsot 104-113
H4 10/7 Homework Assignment # 5
L12 10/11 Euler angles; Relation to \vec\omega; Symmetric top. Small displacements from stable equilibrium 113-124
L13 10/14 Diagonalization procedure; normal modes; molecules 125-132
H6 10/14 Homework Assignment #6
L14 10/18 using fourier trans; Other L's. Loaded and thick strings. 132-136 +
L15 10/21 Field Theory; Three dimensional continua - solids; Equations of Motion 136-142
H7 10/21 Homework Assignment #7
Exam 10/25 Midterm Exam, Sections 1.1 - 5.3
L16 10/28 Fluids. Legendre transforms, 1-forms, 145-154
L17 11/1 complex structure; variations on phase curves; Canonical transformations, 155-159
L18 11/4 Poisson brackets; Jacobi identity; Poisson and Liouville Theorems; 159-166
H8 11/4 Homework Assignment #8
L19 11/8 Higher Differential Forms; Exterior derivative 166-174
L20 11/11 covariance, symplectic form on phase space, d\omega_3 in extended p.s. 175-180
H9 11/11 Homework Assignment #0
L21 11/15 Generating Functions; Canonical Transformations, active and passive; 180-186
L22 11/18 Hamilton Jacobi theory, action-angle vars; 186-195
H10 11/18 Homework Assignment #10
L23 11/29 Integrable systems, example invariant torii; 195-200
L24 12/2 canonical pert. theory; time-dependent pert. theory; (206-213)
H11 12/2 Homework Assignment #11
L25 12/6 Adiabatic variation; (214-226)
L26 12/9 Field Theory, Special Relativity (233-246)
H12 12/9 Homework Assignment #12
L27 12/13 Klein-Gordon, Maxwell Theory (254-260)
Exam 12/21 Final exam, 1:00-5:00 PM, SEC 207 (not ARC!)

Note: Page numbers changed after inserts in November. New pages in (). We should cover all of my book except pages 218-225 (224-231) and, sadly, 240-247 (246-253).

Supplementary Notes

Here are some supplementary notes, some of which may review material we are using in more depth.
  • Notes on totally antisymmetric tensors, or Levi-Civita symbols, εμνρ..., in 3-D Euclidean space: (view), (print), and in higher dimensional Euclidean or Minkowski space: (view), (print), including their use with matrices and determinants. The Levi-Civita symbol is also essential in curved spaces, but that is for another course.
    Also, on ε and determinants, "Properties of Determinants": (view), (print)
  • On Indices and Arguments: (view), (print). Some cautionary notes on how indices are used and how to avoid making nonsense when evaluating expressions with dummy indices.
  • On shortest path with general metric: (view), (print).
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  Joel Shapiro (
  Last modified: Thu Dec 9 09:44:55 2010