# Solution to the Gyroscope

Here is the link to my paper that derives the complete mathematical solution to the gyroscope (the spinning top) in closed form.
http://www.scribd.com/doc/95320068/Solving-the-Spinning-Top
The abstract is,
"The closed form solution is found for the fully nonlinear dynamics of the gyroscope with a fixed point at the tip. The solution is found by using Cardano’s formulae to factor a cubic, in the case where all roots are know to be real. From this, the nutation angle is solved first in terms of Jacobi’s elliptic integral of the first kind. A simple change of variables then transforms the dependent variable of the remaining equations from time to the projection of the nutation angle onto the vertical axis. After this transformation, the remaining equations can be integrated exactly, giving solutions expressed in Jacobi’s elliptic integrals of the third kind. Reduced energy, angular momentum and moment of inertia are defined."
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On Fri, 1 Jun 2012 06:02:43 -0700 (PDT), John Schutkeker

You are not 16 years old, by chance?
w.
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Dear Helmut Wabnig:
On Friday, June 1, 2012 7:10:38 AM UTC-7, Helmut Wabnig wrote:

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Been something if he had done it at the center of mass, or something... since I never see a top spin around a fixed point.
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Probably just OCD, since he feels the need to repost periodically.
David A. Smith
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nice.
thus quoth: roll, pitch and yaw analogy to an airplane is not perfect, because thevehicle would be standing on its nose or tail and spinning rapidly
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Gyro spinning wheel does not fall over as long as its spinning.Reality is its defying gravity. The explanation for this amazing feat lies in the effects of precession. On my 8th birthday I got a gyro. To show my appreciation I gave the world my "Spin is in theory",and structure of electrons. I still have this gyro. I would not part with it for a million bucks. TreBert PS When the gyro starts spinning the whole gyro rotates around the spin axis,which runs along the axle Get the picture
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On 6/8/12 8:39 AM, G=EMC^2 wrote:

Nothing (with mass) defies gravity, Herb. Oh you can argue that a block of wood sitting on the kitchen table is defying gravity. The table is holding up the block with F_net = 0 .
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he is just ear candy for the uneducated. always has been. and when he's right about something, is usually NOT his idea.
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There can be sideways outward weight.
Mitchell Raemsch