Applied Calculus and Gyroscopes

by Ramez Indrawis

 

Submitted : Fall 2020

The objective behind this project is to derive and solve the equation of motion for the spin of a gyroscope in a real-life situation. The gyroscope consists of a lot of separate parts which include the frame, spinning axis, the gimbal and the rotor. Set gyroscope with a specified mass of (m) and moment of inertia, which is (I) for rotating around the axis. However, the rotation on the z-axis will be controlled by another gyroscope to keep it from tilting for the sake of simplicity. The outer frame is attached to the other gyroscope which will be neglected during the calculations in this project. The distance between the pivot and the center of the wheel used in the gyroscope is (d), moreover, that wheel rotates with angular velocity of (ω) about the axis. The rod mentioned makes an angle (θ) while being tilted up with respect to the horizontal. The final variable is gravity, which has a downward force of a specified magnitude (mg).

Related Links: