Modeling and Analyzing the Dynamical Motion of a Rigid Body with a Spherical Cavity

Abstract

AbstractThe rotatory motion of a rigid body having a cavity, close to a spherical form, filled with a viscous incompressible fluid around its center of mass is investigated. It is assumed that the Reynolds number has a modest restricted value due to the high velocity of the fluid. The body rotates under the influence of a viscous fluid besides the action of a gyrostatic moment vector about the principal axes of the body. The governing system of motion is derived and the averaging of the Cauchy problem of this system is analyzed. The analytic solutions are derived through several transformations and plotted graphically to demonstrate the positive influence of the physical body's parameters on the motion. The stability of these solutions is examined through their phase plane diagrams. In light of the efficiency of a gyrostatic moment on the considered motion, new results of this work have been achieved. The significance of this work stems from its numerous uses in everyday life, particularly in vehicles that hold liquids, such as aircraft, submarines, ships, and other vehicles. Moreover, it is also used in engineering applications that depend on the gyroscopic theory.