Instructional Cartoons, Movies and Programs

Field from a uniformly charged plane.

Charge migration to the outside of a sphere.

Multiple masses separated by springs.

Poincare plot of the damped, driven pendulum.

The electric field from a uniformly
charged plane is constant and normal to the plane. The field is normal because
all of the sideways field components cancel out. This process is
demonstrated in this PowerPoint
presentation, and at this URL.

When charge is placed in the interior of
a conducting sphere, the charge will migrate to the outside of the sphere.
There will be no electric fields in the interior. This fact was first
discovered by Ben Franklin, and is illustrated in this PowerPoint
presentation, and at this URL.

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A closed metallic surface will shield out
external electric fields. Such a surface is called a Faraday cage, and
works by the electrons adjusting their position so as the shield the external
charge. See this PowerPoint
presentation, or this URL.

Since a Faraday cage shields out
external electric fields, it can protect objects inside. For example a
person is protected from a lightning bolt inside a car since a car is almost a
complete enclosure. The performer Dr.
Megavolt protects himself from a huge tesla coil with a Faraday cage body
suit. View a dramatic movie
here.

A Brachistochrone is the path between two
positions which a falling particle will traverse faster than any other
path. The program below finds the
path, and compares the traversal time on this path to the time on several other
paths. The program is written in
LabVIEW. If you have LabVIEW,
download the program
library directly (230KB).If you do not have LabVIEW, but have the LabVIEW
6.0 runtime engine, download this executable
(723KB). If you have neither
LabVIEW or the LabVIEW runtime engine, also download the runtime
engine (12.3MB.)

This program plots the orbit or a particle in a central potential . The program is written in LabVIEW. If you have LabVIEW, download the program library directly (152KB).If you do not have LabVIEW, but have the LabVIEW 6.0 runtime engine, download this executable (810KB). If you have neither LabVIEW or the LabVIEW runtime engine, also download the runtime engine (12.3MB.)

This program plots the orbit in a rotating frame of a particle executing a straight line orbit in a stationary frame. The effects of the centrifugal and Coriolis forces is very apparent. The program is written in LabVIEW. If you have LabVIEW, download the program library directly (143KB).If you do not have LabVIEW, but have the LabVIEW 6.0 runtime engine, download this executable (477KB). If you have neither LabVIEW or the LabVIEW runtime engine, also download the runtime engine (12.3MB.)

Epidemics will only spread if a disease is sufficiently contagious. If enough people are immune, the epidemic will not spread because of herd immunity. The spread of an epidemic is described by the math field of Percolation Theory, and can be studied mathematically and by simulation. The program below simulates the spread of an epidemic. The program, written in LabVIEW. If you have LabVIEW, download the program library directly (393KB).If you do not have LabVIEW, but have the LabVIEW 6.0 runtime engine, download this executable (459KB). If you have neither LabVIEW or the LabVIEW runtime engine, also download the runtime engine (12.3MB.)

Tops, gyroscopes, and other mechanical devices are based analyzed in terms of Euler angles, but the angles are hard to visualize. A PowerPoint presentation and this link contain static images and movies of the Euler Angles. (Click on the images in the second through seventh frames to play the movies.)

A string of masses separated by springs models
solids, molecules and other interesting substances. The number of normal modes of a system will equal the number
of masses. This animation
displays the behavior of six identical masses, separated by five identical
springs, and anchored at both ends with the same type of spring.

Computer simulations aid the study of chaos. The damped driven pendulum demonstrates many aspects of chaos. The package of programs below explores the damped driven pendulum, the double pendulum, and the double spring mass systems. The programs are written in LabVIEW. If you have LabVIEW, download the program library directly (621KB).If you do not have LabVIEW, but have the LabVIEW 6.0 runtime engine, download this executable (695KB). If you have neither LabVIEW or the LabVIEW runtime engine, also download the runtime engine (12.3MB.)

The package includes these programs.

1.
**Double Spring Mass: **Linear, two mass, spring mass
system demonstrating that trajectories do not diverge.

2.
**Double Pendulum: **Double pendulum system demonstrating
divergent trajectories.

3. Damped, driven chaotic pendulum:

a.
**Chaotic Pendulum Spectrum Animation: **An animated
display of the chaotic pendulum including the spectrum of the pendulum
response.

b.
**Chaotic Pendulum Phase Space: **An animated display of
the chaotic pendulum phase space.

c.
**Chaotic Pendulum Poincare Animation: **An animated
display of the chaotic pendulum Poincare plot.

d.
**Chaotic Pendulum Poincare Plot:** Quickly generates the
Poincare plot of the chaotic pendulum.
Can store the plot in a file.

e.
**Chaotic Pendulum Poincare Plot Reader:** Displays stored
plots generated by **Chaotic Pendulum Poincare Plot.**

f.
**Chaotic Pendulum Bifurcation Diagram: **Plots the
bifurcations of the chaotic pendulum as a function of g.

g.
**Chaotic Pendulum Basins of Attraction:** For certain
parameter values in the approximate vicinity of 1.29<g<1.47, the pendulum phase will either increase or decrease
steadily. This program plots the
basins of attraction.

h.
**Chaotic Pendulum Fractal Dimension: **Finds the
correlation dimension of the pendulum’s Poincare plot.

i.
**Chaotic Pendulum Winding Number: **The winding number of
the chaotic pendulum.

4. Logistic Map:

a.
**Logistic Map Animation:** An animation of construction of
successive points of the logistic map.

b.
**Logistic Map Poincare Plot: **Generates the Poincare plot
of the logistic map.

c.
**Logistic Map Bifurcation Diagram: **Plots the bifurcation
diagram of the logistic map.

d.
**Logistic Map Lyapunov Scan: **Calculates the Lyapunov
exponent of the logistic map.

e.
**Logistic Map Lyapunov Divergence: **Plots the separation
between two initially close trajectories, and compares the separation to the
predicted Lyapunov separation.

5. Standard Map:

a.
**Standard Map Animation:** An animation of the
construction of successive points of the standard map.

b.
**Standard Map Devil’s Staircase:** Constructs the Devil’s
Staircase of the standard map.

In the chaotic regime, the Poincare plot of the damped driven pendulum is highly folded fractal. This file (18.MB) contains the Poincare plots obtained with several different system parameters. The plots can be enlarged to show the fractal structure. If you have neither LabVIEW or the LabVIEW runtime engine, download the runtime engine (12.3MB.)

The basins of attraction of the damped driven pendulum have fractal boundaries. This link, and this powerpoint presentation, show a set of the basins of attraction as the system drive is increased, and a series of successive blowups of one of the basin boundaries.