Journal of Applied Mathematics
Volume 2012 (2012), Article ID 812645, 14 pages
http://dx.doi.org/10.1155/2012/812645
Research Article
Electromagnetic Gyroscopic Motion
1Mathematics Department, Preparatory Year Deanship, Umm Al-Qura University, P.O. Box 5555, Makkah 21955, Saudi Arabia
2Faculty of Science, Tanta University, P.O. Box 31527, Tanta, Egypt
3Mathematics Department, Faculty of Girls Education and Science, Taif University, Al-Khurmah Branch, P.O. Box 888, Taif 21974, Saudi Arabia
4Electricity Department, Faculty of Engineering, Umm Al-Qura University, P.O. Box 5555, Makkah 21955, Saudi Arabia
Received 31 July 2012; Revised 22 October 2012; Accepted 12 November 2012
Academic Editor: Francesco Pellicano
Copyright © 2012 A. I. Ismail et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
A problem of the gyroscopic motions around a fixed point, under the action of a gyrostatic moment vector, in presence of electromagnetic field and Newtonian one, is considered. The small parameter technique is used to investigate the periodic solutions for the derived equations of such motion problem. A geometric interpretation of motion will be given in terms of Euler’s angles (). Computer programs are carried out to integrate the attained quasilinear autonomous system using a fourth-order Runge-Kutta method. A comparison between the obtained analytical solutions and the numerical ones is investigated to calculate the errors between them.