What is the math of this effect?

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The discussion centers on an experiment involving a gyroscope that appears to exhibit reduced mass, prompting inquiries about the formal name of this effect and the mathematical principles behind it. The user seeks resources to understand the calculations involved, particularly regarding the gyroscope's behavior when orbiting in a circle. Three methods for calculating the gyroscopic effects are identified: using torque and angular momentum, applying spherical coordinate systems, and employing Euler-Lagrange equations. The latter two methods are noted as being similar, with the third being the more straightforward approach. Overall, the conversation highlights a keen interest in the mathematical underpinnings of gyroscopic motion.
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On http://www.gyroscopes.org/1974lecture.asp during segment 8 (from 2:18) an experiment with a gyroscope is conducted.

This is the clip of just that experiment

The gyroscope apparently has less mass. Where can I find math to describe this effect? What is this effect called formally?

Additionally, if this gyroscope were additionally orbiting in a circle with axis parallel to the gyro's axis of rotation, how would the effective centrifugal force of the gyro be calculated?
 
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Very cool experiment! I'd be interested in the math as well.
 
There's 3 different ways of doing the maths that I know of:
1) use the rules of torque, angular momentum, etc
2) simply calculate what happens in a spherical coordinate system (there will be real forces and fictitious forces)
3) use euler-lagrange equations

2 and 3 are effectively the same thing, but 3 is probably easier. 1 comes from 2 and 3.
 

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