Nonlinear Dynamical Motion of a Nearly Spherical Gyrostat Containing a Spherical Slug Filled with a Viscous Liquid

Abstract

Abstract The present work is concerned with the nonlinear dynamical motion of a quasi-spherical gyrostat containing a spherical slug filled with a viscous fluid. The governing system of nonlinear equations is derived and subsequently transformed into a non-dimensional form. The average method is used to approach a solution for the system. To stand on a small parameter in the problem, the Reynolds number is assumed to be tiny and yet implies that the kinematic viscosity coefficient is too large, for which its inverse quantity is chosen to be the small parameter. The body’s motion is influenced by torque from the internal liquid and by the gyrostatic torque (GT). By applying the averaging method to the non-dimensional equations, we eliminate the effects of the first two GT components, leaving only the influence of the third component. The influence of the third torque component is demonstrated through graphical simulations to analyze the body’s motion under various values of this torque. The obtained outcomes have practical applications in fields such as spacecraft spin-stabilization with propellant slosh, the modeling of Earth-core wobble and planetary nutation, and the design of high-precision, fluid-damped gyroscopes and stabilizers.