RAP TRANSPARENCY • Rhythmic Juggling Rap
Scientist P. J. Beek studies harmonic wave motion of objects and hands.
SECOND TRANSPARENCY • General Tessellation
He made "time tessellations" like this graphed model where:
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.
THIRD TRANSPARENCY • Beek considered a ratio k
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 tward k = 1/2.
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.
ACTION Show two graphs together then separate them to point out the following and put S's graph in hand out:
FOURTH TRANSPARENCY • Tessellation For k = 3/4, the toss is made 2/3
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.
ACTION Point to the locations on the graphs as presented or mark them with color.
FIFTH TRANSPARENCY • Tessellation For k = 1/2, the pattern is: toss when
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.
SIXTH TRANSPARENCY • a double harmonic oscillator
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.
• The Juggling Talk Outline
•Chautauqua Basic Juggling
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