The science of skill

I was bored whilst working on my thesis, and found this delightful
article in the American Journal of Physics. Unicycling.org was the
first reference used in the paper!

-Abstract:-
*A model of balancing upright on a unicycle has pitchfork and Hopf
bifurcations, and describes riders from novice to expert with both
good and not-so-good reactions.*


The author suggests a new metric with which to judge a rider's skill.
He has come up with the "unicycle equation of motion," a second-order
linear diff. eqn., which has terms that describe the rider's reaction
time and ability to "self-excite" and control oscillations about
equilibrium.

*
INTRODUCTION
There is no real mystery about how unicyclists stay
upright—they pedal so as to keep their point of contact with
the ground under their center of gravity.
But pedaling is confined to the plane of the wheel, and so
a sideways fall has to be countered by first turning the wheel plane.
This may be done by upper-body rotation, using angular momentum
conservation and wheel/ground friction.
As a result, a competent rider can control the machine near
upright by continual small adjustments of the wheel plane
plus minor pedaling to and fro. This may be either static
balancing (‘‘idling’’) or a subsidiary component of steady
progress.
(snip)

CONCLUSION
Finally, we have the model of Eq. (11), which for various
values of parameters (a,b,c) includes all cases considered,
and describes the essential planar part of the unicycle balancing
mechanism.
It accommodates the spectrum of riding ability, including
unicyclists with both perfect and, more realistically, somewhat
imperfect reactions.
Quite reasonably, it shows that any small time lag in the
rider’s reactions tends to increase the instability of upright
equilibrium. However, expert riders may exploit this to show
off their skill.
(snip)*


Leave it to scientists to take something fun and make it as dry as burnt
toast.


--
maestro8 - Mad Scientists for World Domination

Those are my principles. If you don't like those, I have others. --
Groucho Marx
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THERE IS NO REAL MYSTERY ABOUT HOW UNICYCLISTS STAY
UPRIGHT—THEY PEDAL SO AS TO KEEP THEIR POINT OF CONTACT WITH
THE GROUND UNDER THEIR CENTER OF GRAVITY.
BUT PEDALING IS CONFINED TO THE PLANE OF THE WHEEL, AND SO
A SIDEWAYS FALL HAS TO BE COUNTERED BY FIRST TURNING THE WHEEL PLANE.
THIS MAY BE DONE BY UPPER-BODY ROTATION, USING ANGULAR MOMENTUM
CONSERVATION AND WHEEL/GROUND FRICTION.
AS A RESULT, A COMPETENT RIDER CAN CONTROL THE MACHINE NEAR
UPRIGHT BY CONTINUAL SMALL ADJUSTMENTS OF THE WHEEL PLANE
PLUS MINOR PEDALING TO AND FRO. THIS MAY BE EITHER STATIC
BALANCING (‘‘IDLING’’) OR A SUBSIDIARY COMPONENT OF STEADY
PROGRESS.

this would make a good back of a T-shirt


--
Brian MacKenzie - LAN Solo

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Do you have a link to the article?


--
Ben Plotkin-Swing

www.benps.com

"Every truly great accomplishment is at first impossible" -Fortune
cookie.
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Looks like this is the citation: R. C. Johnson (Department of
Mathematical Sciences, University of Durham, Durham DH1 3LE, United
Kingdom), "Unicycles and bifurcations," American Journal of Physics --
July 1998 -- Volume 66, Issue 7, pp. 589-592


--
tadaniels - USA President
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tadaniels wrote:
*Looks like this is the citation: R. C. Johnson (Department of
Mathematical Sciences, University of Durham, Durham DH1 3LE, United
Kingdom), "Unicycles and bifurcations," American Journal of Physics --
July 1998 -- Volume 66, Issue 7, pp. 589-592 *


To answer Ben, this is the correct article, however, it is only
available for access with a subscription. Most university libraries
subscribe to online journal services; if you can't find the journal in
their stacks, ask a librarian about accessing the journal online.


--
maestro8 - Mad Scientists for World Domination

Those are my principles. If you don't like those, I have others. --
Groucho Marx
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maestro8 wrote:
*I was bored whilst working on my thesis, and found this delightful
article in the American Journal of Physics. Unicycling.org was the
first reference used in the paper!



The author suggests a new metric with which to judge a rider's skill.
He has come up with the "unicycle equation of motion," a second-order
linear diff. eqn., which has terms that describe the rider's reaction
time and ability to "self-excite" and control oscillations about
equilibrium.



Leave it to scientists to take something fun and make it as dry as
burnt toast. *


Wow, Jason, it looks like finals for you are finally over...


--
gerblefranklin - Trials Unicyclist

http://gallery.unicyclist.com/Trials-Muni

"Peace cannot be kept by force. It can only be achieved by
understanding."-Albert Einstein
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gerblefranklin wrote:
*Wow, Jason, it looks like finals for you are finally over... *


YEE HAW!

Even better, UPS will deliver my trials Yuni this Friday! Looks like
Christmas is coming early this year.


--
maestro8 - Mad Scientists for World Domination

Those are my principles. If you don't like those, I have others. --
Groucho Marx
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Google reveals that the article is available online:
http://maths.dur.ac.uk/~dma0rcj/PED/uni.pdf


--
dogfeathersvt - Former Newbie
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On Wed, 8 Dec 2004 20:04:49 -0600, "dogfeathersvt" wrote:

Google reveals that the article is available online:

And if you're done reading that and then still crave for more, check
out Mike Penton's list of links at
http://mike.hinson.unicyclist.com/. It includes the article this
thread started with.

Klaas Bil - Newsgroup Addict
--
"Deflating pi does not reduce calories, it just concentrates them. - billham"

O wow, I'm going to have to read that in more detail. I do love my
differential equations! ! !

Be sure to post your thoughts about the article as people read it.

Ouch, time to go dream about thermodynamics.


--
Bob22b - MCL Tearer :d
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