Instructional Cartoons, Movies and Programs

Field from a uniformly charged plane.

Charge migration to the outside of a sphere.

Faraday Cage.

Faraday Cage-Dr. Megavolt.

Brachistochrone.

Orbits in central forces.

Orbits in rotating frames.

Spread of epidemics.

Euler angles.

Multiple masses separated by springs.

Chaotic Pendulums.

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.