Most general gyroscope motion

Asked Dec 01 '14 at 16:05

Active Dec 01 '14 at 18:06

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In Kleppner & Kolenkow's Introduction to Mechanics (Amazon link), the general gyroscope motion including nutation was derived using the approximation condition $\Omega T \ll 1$ where $\Omega$ is the precession angular velocity and $T$ is the period of nutation.

How does one describe the gyroscopic motion if the the condition for the approximation is not satisfied? How does one describe the general gyroscopic motion if

the angular momentum of precession is not negligible and
if the gyroscope spins very slowly around its axis, $\omega$ is low?

In general I want to find the formula for most general gyroscope motion. If I let $\omega$ go to zero then I should get the special case of a pendulum.

edited Dec 01 '14 at 18:06

Kyle Kanos

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asked Dec 01 '14 at 16:05

user50224

possible duplicate of Describing a motion of gyroscope with gimbal – John Alexiou Dec 01 '14 at 21:09
See also related post: http://physics.stackexchange.com/a/80449/392 – John Alexiou Dec 01 '14 at 21:10
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I actually think this may not be a duplicate, since the other question is just asking how to describe ordinary gyroscopic motion, whereas this one is asking how to go beyond that and relax the assumption that $\Omega T\ll 1$. (Besides, this question is much better phrased than that one.) – David Z Dec 02 '14 at 05:13
@DavidZ: Thanks for recognizing that my question is different. Have you also got some clue or an answer for me? – user50224 Dec 02 '14 at 14:52

Most general gyroscope motion

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