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.
formatting link

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=92s 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=92s 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=92s elliptic integrals of the third kind. Reduced
energy, angular momentum and moment of inertia are defined."
Reply to
John Schutkeker
Loading thread data ...
You are not 16 years old, by chance?
Reply to
Helmut Wabnig
Dear Helmut Wabnig:
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.
Probably just OCD, since he feels the need to repost periodically.
David A. Smith
Reply to
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
Reply to
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
Reply to
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 .
Reply to
Sam Wormley
he is just ear candy for the uneducated. always has been. and when he's right about something, is usually NOT his idea.
Reply to
Raymond Yohros
There can be sideways outward weight.
Mitchell Raemsch
Reply to

PolyTech Forum website is not affiliated with any of the manufacturers or service providers discussed here. All logos and trade names are the property of their respective owners.