368(8): The Analytical Mechanics of Torque in a Gyroscope

In this note it is shown that a gyroscope can be weightless under condition (40). The three torques in frame (1, 2, 3) of the principal moments of inertia can be worked out from the Euler angles as shown. This is to complicated to be done by hand, but can be done by computer algebra. The torque magnitudes in frames (1, 2, 3) and the lab frame (X, Y, Z) are related by Eq. (28). As is well known, the gyro does not fall over because it generates an upward force which can be defined in terms of the torques of frame (1, 2, 3) as in Eq. (32). Finally, in certain configurations such as that demonstrated by Laithwaite, the gyro appears weightless. This is very useful in mecahnical engineering and probably in aerospace engineering.


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