368(5): Complete Dynamics of the Gyro

These are found from Eqs. (27), (28) and (29) in the three Euler angles sketched in Figure (1). These are simpler and clearer solutions than those given by Marion and Thornton. It would be very interesting to graph and animate these motions, found by the three Euler Lagrange equations in the three Euler angles. It is found that the Euler angle psi increases monotonically with time. The motion of the Euler angle theta is governed by Eq. (27), which may or may not have an analytical solution but can easily be solved by computer, bearing in mind that theta is a function of time. Finally the Euler angle phi can be found from Eq. (28) give the solution for theta(t). This completes the baseline calculation. We are now ready to add another force in the positive Z axis, and graph and animate the elevation of the point of the gyroscope in order to compare (at least in outline) with the experimental data of Laithwaite and Shipov. This is teh overall aim of UFT367and UFT368.

a368thpapernotes5.pdf

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