Application of Krylov–Bogoliubov–Mitropolski method to asymmetric gyrostatic 3D motion in multi-fields
T. S. Amer, A. H. Elneklawy, H. F. El-Kafly
Abstract
The 3D rotary movement of an asymmetric rigid body (RB) in space around a fixed point is investigated. A gyrostatic torque (GT), a magnetic field (MF), and a Newtonian force field (NFF) all have an impact on the RB's ability to rotate. Around its minor axis of inertia, the body is thought to begin moving rapidly. The Krylov-Bogoliubov-Mitropolski (KBM) method is used to solve the governing equations of motion (EOMs) analytically once they are created using Euler-Poisson equations. Additionally, Euler angles approximate analytical solutions (AS) are examined. A graphical simulated viewpoint of the obtained results and the equations of Euler angles, which show how the body is orientated at each given moment, are used to debate the interpretation of the motion. Maintaining control over the body's rotation and position during motion can be achieved by researching the effects of different values of the acting forces and toques, such as the GT, MF, and NFF. To illustrate how the stability of the RB is affected, phase graphs of various solutions have been created. Periodicity behavior is demonstrated by the closed-phase curves' symmetry around any of their axes. Together with the beneficial impacts of these forces and torques, the movement behavior of the RB is evaluated and simulated. The results obtained are widely relevant to gyroscopic equipment, especially those that incorporate inertial systems like aircraft and satellites. Technologies that guarantee the motion stability of applications are also included.