"Out Juggling In My Class" by William V. Thayer

Act 10. JUG:010 Rhythmic Juggling

copyright © 1996 Wm. V. Thayer, All Rights Reserved



RAP E.

Scientist P. J. Beek studies harmonic wave motion of objects and hands. We are going to look at only the UNIT JUGGLE (16 inch high) case in this discussion.

He made "time tessellations" like this graphed model where:

General Tessellation

The top three curves show a red, yellow or green object's flight record.

and

The bottom two curves show the left and right hand movement.

Beek considered a ratio, k, of dwell time divided by hand cycle time.

Hand cycle time is the sum of the vacant time and dwell time so:

k = D/(V + D)

His research indicated that a novice juggler tended to have k around 3/4.

While more experienced jugglers tended to use ratios, k, closer to 1/2, 5/6 or 2/3.

You can tell the difference between these ratios by looking at two time tessellation models.

They arise from a substitution of each ratio into Shannon's special case equation. As you can tell from this table.

Show two graphs together then separate them to point out the following and put S's graph in hand out:

Tessellation k = 3/4

For k = 3/4, the toss is made two thirds into the last ball's flight time.

This is a sixth of the flight time past the last ball's peak.

Point to the locations on the graphs as presented or mark them with color.

Tessellation k = 1/2

With k = 1/2 the pattern is: toss when there is a peak, in other words, half way through the flight of the last ball.

Here is a Computer Assisted Lab (CBL) Project designed to measure Vacant and Dwell times to find your k values. It uses a joystick port on your computer and you need to make some gloves. See how close you get to P. J. Beek's theory!

A novice and an experienced juggler differ by how one's nervous system links the wave motion of the flying objects with the wave motion of the moving hands.

Here is a physical model of a double harmonic oscillator.

Notice that as I set one object in motion the other object starts moving.

Some energy of one is transferred through this linking bar to the other object.

Ho, the first object has stopped!

Amazing - all of the energy of this object is now in the motion of the other.

So we have an elementary picture of how jugglers manage to juggle.






•Act 11.


•Back to the course catalog.



For more information please contact: William V. Thayer, Mathematics Department, St. Louis Community College at Meramec, 11333 Big Bend Blvd., St. Louis, MO 63122-5799, Telephone 314 984 7866 office
email: thayer@stl-online.net, home page: http://www.stlcc.cc.mo.us/mc/users/thayer

Copyright © 1996 William V. Thayer, All Rights Reserved


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