Modeling of the Euler-Poisson Equations for Rigid Bodies in the Context of the Gyrostatic Influences: An Innovative Methodology

Abstract

This paper presents an alternative approach to solving Euler-Poisson’s dynamical equations, which describe the governing equations of how a rigid body (RGB) rotates around a stationary point with the influence of a gyrostatic moment (GM). The RGB’s angular velocity vector components in our solution are different from those in the well-known cases. It is expected that the RGB’s center of mass lies in the meridional plane along its principal axis of inertia. Additionally, it is assumed that the main inertia moments correspond to a fundamental algebraic equality. Additionally, there is a constraint on the first condition selection. The analytical solution of the problem is provided and depicted graphically using a computer codes, allowing us to analyze the motion at any given time. The influence of distinct values of the GM on these solution are also presented. One could consider the solution to be an entirely novel iteration of Euler’s original case. Solving this equation is crucial due to its broad range of applications, including the design and development of stability enhancement systems in automobiles, dynamics-based sensors like gyroscopic sensors, the analysis of space objects and robotic systems, and gaining insight into the complex movements of RGBs.