Simulation of a Subjected Rigid Body Motion to an External Force and Moment

Abstract

Abstract Purpose This work intends to investigate the rigid body’s motion around a specific fixed point (analogous to Lagrange’s scenario) in the presence of a gyrostatic moment (GM) besides the attraction of a Newtonian force field (NFF). This task is carried out by presuming that the body is quickly rotating about one of the major or minor principal axes of the inertia ellipsoid. Method The controlling system of six nonlinear differential equations (DEs) along with three first integrals is boiled down to an appropriate system of two DEs in addition to only one integral. Therefore, the analytic solutions of this system are obtained utilizing the approach of Poincaré small parameter (APSP). Results Euler's angles for the motion under investigation are derived to assess this motion at any instant of time. Additionally, phase plane graphs are displayed using computer codes to depict the stability behavior of the dynamical motion at any time. Conclusion These achieved outcomes are thought of as a generalization of the ones that were found in some of previous works, in the absence of all applied forces and moments. This work presents a distinctive contribution in several crucial areas, particularly in engineering applications that have used the gyroscopic theory to determine the orientation and maintain the stability of various vehicles, such as spaceships, airplanes, submarines, and racing cars.