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

Abstract

The 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.

Dynamical analysis of a rotating rigid body containing a viscous incompressible fluid

“…These solutions are represented in some plots to display the positive impact of the applied moments and forces on the body’s dynamical behavior. The acquired outcomes are regarded as a generalization of those that were previously obtained for the situation of a null value of the GM other than an uncharged body (Akulenko et al , 2020; Akulenko et al , 2019; Farag et al , 2022). The graphs have clearly shown the positive effects of the fluid’s density, the third projection of angular velocity and the values of the inertia’s main moments, charge and the GM.…”