User:F=q(E+v^B)/Mathematics of juggling

Juggling represents physical and mathematical concepts, in the form of patterns. In the juggling community, there is the siteswap notation which can logically desrcibe most (but not all) juggling patterns, and diagrammatically there are spacec-time diagrams (for juggling, not the same as Minkowski's light cone]]). In addition - there have been attempts to describe juggling in more formal ways: to relate the number of props thrown and hands or people that throw, the geometry of throwing, and the timing of the tosses.

The Shannon equation
The following equation was


 * $$(F+D)H=(V+D)N\,\!$$

where (in his notation):
 * F = Flight time (time a ball is in the air i.e. out of hands),
 * D = Dwell time (time a ball is in contact with hands),
 * H = Hand number (total number of hands manipulating the pattern),
 * V = Vacant time (time a hand is empty),
 * N = Number of balls juggled.

Here is what the equation means.

H and N are dimensionless numbers. D, F, V are times, e.g. measured in seconds.

The total number of hands manipulating the balls is H, from any number of people contributing to the pattern. If one person juggles, H can be 1 or 2. If more people were to enter the pattern H can be greater than or equal to 2.

The total time taken for all balls to be in contact with all hands, and thrown up in the air, is F + D.

The total time taken for a ball to not be in contact with any hands and thrown up in the air, i.e. time taken when no hands are on any balls, is V + D.

If F + D > V + D, i.e. (subtracting D from both sides) F > V, the juggler has the ball in his/her hand for a longer time then when a ball is not in any hand, the pattern is slower. Likewise F < V implies the juggler has the ball in his/her hand for a shorter time then when a ball is not in any hand, the pattern is faster.

As the throw hieght inreases, F increases, the ball is in the air for longer.

As the pattern becomes faster, D decreases and V increases, the balls are in the hands less and not in the hands for longer.