FORCED GYROSCOPIC MOTIONS
A. I. ISMAIL *
Department of Mechanics, Collage of Engineering and Islamic Architecture, Umm Al-Qura University, Makkah, Saudi Arabia and Faculty of Science, Tanta University, Tanta, P.O.Box 31527, Egypt
*Author to whom correspondence should be addressed.
In this work, we consider a forced problem of a gyroscopic motion about a point Ο, which be fixed, in presence of a gyro momentum action, electromagnetic and Newtonian fields. Consider the spring force, Lorentz force, and Newtonian one act upon the gyro. We apply the method of the small parameter for solving the considered problem when the gyro rapidly spinning about the principal axis Z . We apply Euler’s angles (θ,Ψ,∅) to describe the motion of the gyro. Use a Computer description to investigate the obtained analytical solutions according to the characterized parameters of the motion. We integrate the quasi-linear autonomous system for the considered problem numerically to represent the considered solutions. We compare the obtained numerical solutions with ones obtained by the small parameter method to check the accuracy of our solutions. We deduce the influence of the forces parameters on the motion and the stability of the precession.
Keywords: The rotational motions, the gyroscopic motions, moments of inertia, satellites, antennas, solar power collector systems