## PHY4222 Mechanics 2 - Spring 2015

**1. Noether's
theorem**

**2.
Biographies**

**3. The tide prediction for D-Day
**

Physics Today article by Bruce Parker

**4. Foucault's
pendulum**

Wikipedia article with an animation

YouTube video (Foucault's pendulum in the Houston Museum of Natural Science)

**5. Free precession
applet**

**6. Three
body problem in
gravitation**

Eugene Butikov's applet (applet 1 contains chaotic examples shown in class)

David Harrison's applet (shown in class)

**7. Driven
damped pendulum applets**

In this applet, use the default values m=1, L=1, and g=1. Then omega0 will be 1, and the "damping" will be Taylor's 2beta. Since omega0=1, Taylor's choice beta=omega0/4 will correspond here to "damping"=0.5, the default value. Also, since omega0=1, the "drive frequency" will be Taylor's omega/omega0. His choice omega0=1.5*omega will therefore correspond to "drive frequency"=1/1.5=0.6666..., also the default value. omega0=1 also makes the "drive amplitude" here the same as Taylor's dimensionless parameter gamma.

Examine the angle phi as the function of time and also the angular velocity phi-dot as a function of angle phi for the following values of the drive amplitude:

0.9 (see Taylor's Fig. 12.3 on page 466)

1.06 (see Fig. 12.4 on page 467)

1.073 (see Fig. 12.5 on page 471 for gamma=1.07)

1.077 (see Figs. 12.7 and 12.8 on page 471) You will need patience plus many trials to see the period 3 behavior observed by Taylor.

1.081 (see Fig. 12.8 on page 472)

1.0826 (see the same figure) In the applet, you will probably have to look at the phi-dot vs phi graph.

1.105 (see Fig. 12.10 on page 476)

1.13 (see Fig. 12.24 on page 481)

1.15

1.35

1.4 (see Figs. 12.25 and 12.26 on pages 492 and 493)

1.45

1.503 (see Figs. 12.15 and 12.16 on pages 482 and 483)

Nasser Abbasi's program for CDF Player

Download this program, which shows Poincare section and bifurcation map, in addition to a phase-space plot (phi-dot vs phi) and a time series. Note that the bifurcation map here is phi-dot vs drive amplitude, not phi vs drive amplitude. Similarly, the time series is phi-dot vs time, not phi vs time.

The applet used in class can be download from here.

**10. Websites of chaos and nonlinear-dynamics
research groups**(a random selection)

Last updated: 10/16/2014