Lecture 43: Chaos III (14 Dec 09) A. Extend: mechanics models
1. Refs: Goldstein Chapter 11, P. Cvitanovic, Universality in Chaos (reprint collection, 1984), FW Supplement. 2. Much of the language of
Lecture 31: Strings II (13 Nov 09)
Move Set VIII to Nov 23?
A. Continuum string
1. The Lagrangian density for transverse (u) vibrations of a 1D string with mass density and spatially varying tension (
Lecture 30: String I (11 Nov 09) review 9 Nov HW HJ theory of oscillator A. Review continuum string
1. FW Secs. 25 and 38; G Sec. 13.2 2. The Lagrangian density for transverse (u) vibrations of a 1D s
Lecture 28: Hamiltonians (6 Nov 09) A. Hamilton equations
1. In Lagrangian formulation the independent variables are (generalized) coordinates q and velocities q . In the Hamiltonian formulation, they
Lecture 27: Hamiltons equations (4 Nov 09) Review 2 Nov homework A. Review Hamiltonian
1. FW Secs. 18 and 20 and L11 2. In the case that the Lagrangian has no explicit time dependence, L = L(cfw_qj ,
Lecture 26: Top with gravity (2 Nov 09) A. Review: Euler angles
1. Three successive rotations to get to the principal axes of the moment of inertia tensor: (1) by angle around the original z = e0 , (2
Lecture 25: Euler angles (30 Oct 09) A. Euler angles
1. FW sec 29. Start from a set of (inertial) Cartesian axes (0 , e0 , e0 ) e1 2 3 2. Three successive rotations to get to the principal axes of the
Lecture 24: Euler equations exs (28 Oct 09) A. Review: Eulers equations
1. Calculate the time derivative of angular momentum relative to the center of mass in terms of torques dL dL |inertial = |body
Lecture 32: Membranes (16 Nov 09)
Homework Set VIII will be due Nov 23, not Nov 30.
A. Hamiltonian theory
1. FW Sec 45. Example of constructing an equation with a current to balance a conservation law
Lecture 33: Hydrodynamics (18 Nov 09) A. Beginnings
1. FW Sec. 48 2. This is an ad hoc approach to the dynamics of a continuous uid. More systematic (statistical physics) approach starts from the N -p
Lecture 34: Hydrodynamics II (20 Nov 09) A. Review: density and momentum
1. Consider small volume element xed in space, the change within, and the ows across the bounding surface. 2. Equation of conti
Lecture 42: Chaos II (11 Dec 09)
lecture 41 on FPU plus the Dung oscillator pp. 52-58 of FW supplement.
A. Dung oscillator
1. One-dimensional nonlinear model oscillator 1 1 V (q ) = mq 2 + mq 4 2 4 St
Lecture 41: Chaos I (9 Dec 09)
Final exam: take home distributed Dec 14, due 1PM Dec 21, limit 72 hours of work.
Review 7 Dec homework A. Introduction
1. Ref linked to text: Fetter and Walecka, Nonlin
Lecture 40: Electrodynamics II (7 Dec 09) A. Review Electrodynamics
1. Recall: 4-vector transforms as A =
a A
and that x = (ct, r) is a 4-vector. 2. Lorentz invariance of scalar products of two 4-vec
Lecture 39: Electrodynamics (4 Dec 09)
Project: 2 homework-like problems from Fetter-Walecka or Goldstein on under-represented topics in the homework, for instance Hamilton-Jacobi theory, continuum me
Lecture 38: Relativistic mechanics (2 Dec 09)
Project: 2 homework-like problems from Fetter-Walecka or Goldstein on under-represented topics in the homework, for instance Hamilton-Jacobi theory, conti
Lecture 37: Four-vectors (30 Nov 09)
Homework for December 7 is available as Supp09.pdf and ps.
A. Review: Lorentz transformation
1. Frames S and S moving with relative velocity v along x ct = (ct x)
Lecture 36: Lorentz (25 Nov 09)
homework for Dec 7 is SUPPL09.pdf, *.ps. Review 23 Nov homework.
A. Lorentz transformation review
1. Barger-Olsson Mechanics Sec.10.3. Special geometry: relative motion
Lecture 35: Relativity (23 Nov 09) A. Galilean transformations
1. Refs: Goldstein Chapter 7, Bergmann Chap 2, Mller Chap 1 2. Inertial frame: in such a coordinate system all bodies not subject to forc
Lecture 23: Euler equations (26 Oct 09) A. Review: Eulers equations
1. Calculate the time derivative of angular momentum relative to the center of mass in terms of torques dL dL |inertial = |body + L
Lecture 22: Rigid body rotations (23 Oct 09)
Kepler ellipse averages: Angle average r = a 1 r 1/ (1/r) = a
2.
t-averages :
A. Review/completemoment of inertia
1. Start with case of no net translation
Lecture 9: Lagrange I (23 Sep 09) 0. review 21 Sep HW A. Review: constraints
1. Restrictions on the N -particle motion so that there are fewer than n = 3N independent degrees of freedom. 2. There are
Lecture 8: Constraints (21 Sep 09) A. Falling body
1. Vector directions using spherical polar coordinates and assuming spherical earth r, , , = z . Cross products: r = ; = r; r = cyclic 2. For the ang
Lecture 7: Rotations II (17 Sep 08) A. Complete L6.B
1. Express the dierential of the dot products as: dei ei = 0 = 2i dei e dei ej = 0 = ei dej + ej dei ei dej = ej dei 2. Expand the dierentials in p
Lecture 6: Rotations I (16 Sep 09) 0. review homework
The homework is posted and can be accessed from the below link, after login to MyUW to view the contents. https:/www.library.wisc.edu/course-pages
Lecture 2: Two-body problem (4 Sep 09) A. Relative motion of two bodies
1. Use notation R R [bold face for vectors] so that dot for time deriva tive is R. 2. Formulate Newtons laws using two bodies wi