505 (AU06) Daily lecture topics

What was covered in lectures ( in red), and material not covered but which you should read.

Lecture	Date	Covered in lecture	Reading (not covered)
1.1	9/27	Class organization. FW 1.1-1.2: review of Newton's laws.
1.2	9/29	FW 1.2-1.3. Energy, 1-d problems Begin 2-d single particle problem.	Reduced mass.
2.1	10/2	FW 1.4 Orbits
2.2	10/4	FW 1.5 Scattering
2.3	10/6	FW 2 Non-inertial frames
3.1	10/9	FW 2 (concluded) Applications of fictitous forces
3.2	10/11	FW 3 (secs 17,18) Introduction to Lagrangian mechanics Principle of least action for unconstrained system Calculus of variations
3.3	10/13	FW 3 (secs 17, 13, & 14) Example of "brachistochrone" (calc. of var.) Generalized coordinates, holonomic constraints
4.1	10/16	Deriving Euler-Lagrange equations for constrained motion Method (i) enforce constraints with coords Leads to FW eq. 15.22	Steve Ellis's lecture 3
4.2	10/18	Deriving Euler-Lagrange equations for constrained motion Method (ii) Lagrange multipliers (FW 19) Example of bead on wire	Examples in FW 19
4.3	10/20	Non-conservative forces (FW 15) Velocity dependent potentials	Steve Ellis's lecture 7
5.1	10/23	FW 20 Conjugate momenta and conservations laws Hamiltonian function	Example at end of FW 20.
5.2	10/25	FW Ch 4, secs 21-22 Small oscillations	Coupled pendula example, sec 23
5.3	10/27	FW Ch 4, sec 22 (finish) Mathematics of small oscillations Apply to triatomic molecule
6.1	10/30	FW Ch 4, secs. 24/25 Sending N to infinity ("continuum limit")	sec. 24: calculating the determinant for any N sec. 25: Normal coordinates in the large N limit
6.2	11/1	Finish FW Ch 4, sec. 25 (Hamilton's principle in continuum limit) Begin FW Ch 5, secs. 26/27 Rigid body motion Inertia tensor
6.3	11/3	FW ch 5, secs. 26 (continued) 27/28/29 Principal axes, Euler's equations Stability of torque-free motion Euler angles	sec. 26: Parallel axis theorem sec. 28: first three examples
7.1	11/6	Applications of Euler angles: FW 30 & 31 Wobbling football/earth Precession and nutation of symmetric top with fixed point.	I only provided a sketch of the analysis See FW for more details.
7.2	11/8	Hamiltonian mechanics: FW 32	FW 33: example of EM interactions For example of spherical coordinates, see Ellis lecture 11.
7.3	11/10	HOLIDAY!
8.1	11/13	FW 34: Canonical transformations FW 35: Hamilton-Jacobi equation
8.2	11/15	Midterm
8.3	11/17	FW 35: Hamilton-Jacobi equation Relation to QM	FW 37: Poisson brackets
9.1	11/20	Midterm discussion A little more on the Hamilton-Jacobi equation and its relation to QM Overview of upcoming discussion of chaos Anharmonic oscillator and flow in phase space	Baker and Gollub: Chs 1 and 2
9.2	11/22	Phase space flows for anharmonic oscillator and undamped pendulum Hamiltonian flow as that of an incompressible fluid Flows for damped pendulum and attractors (see Mathematica notebook ).
9.3	11/24	HOLIDAY!
10.1	11/27	Forced damped pendulum and limit cycles Poincare maps Mathematica notebook used in class.	Baker and Gollub Ch 3
10.2	11/29	Finish phenomenology of forced, damped pendulum Bifurcation diagram, period doubling route to chaos, winding number Mathematica notebooks used in class: Bifurcation plot and winding number , phase plots and Poincare sections (an extension of the notebook from last lecture).	Baker and Gollub Chs. 4 and 5
10.3	12/1	Logistic map as a model for route to chaos Self-similarity, understanding bifurctions with return functions Mathematica notebooks used in class: playing with the map , and return functions .
11.1	12/4	More on the logistic map Bifurcation in detail Calculating Lyapunov exponents Intermittency Used Mathematica notebooks from last class	Entropy characterization of chaos (BG 4.1.4)
11.2	12/6	Definitions of fractal dimension Fractal dimension of strange attractors Evaluations
11.3	12/8	Discussion of final exam Summary of what we have learned about chaos Survey of experimental examples [Standard circle map and frequency locking (notebook) .]	For fun: Chs 6 and 7 in BG

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Stephen Sharpe

Last modified: Tue Sep 11 16:22:24 PDT 2007