article · European Journal of Pure and Applied Mathematics
This research outlines an alternative analytical method for solving the Euler-Poisson dynamical equations, which govern the rotation of a rigid body around a fixed point subject to a gyrostatic moment. In this framework, the rigid body has its centre of mass positioned in the meridional plane along a principal axis of inertia, with its main moments of inertia satisfying a specific algebraic equality. The resulting components of the angular velocity vector diverge from established traditional cases, offering a new iteration of Euler's classical problem. Computer code provides graphical depictions of the analytical solutions, enabling the motion to be evaluated at any point in time. The study also demonstrates how differing values of the gyrostatic moment influence the overall rotational behaviour.
Understanding how objects spin and stabilise under internal or external forces is fundamental to mechanics. Providing a fresh mathematical solution for rotating bodies influenced by gyrostatic forces helps engineers and scientists accurately predict and model complex motions, which is essential for designing dependable moving machinery, guidance instruments, and automated systems.
The mathematical model has relevant applications in designing vehicle stability enhancement systems, gyroscopic sensors, robotics, and space object analysis. Potential users include aerospace engineers, sensor developers, and automotive control systems designers. However, because the abstract presents only an analytical solution verified by computer graphics, the technology sits at an early theoretical stage, requiring practical testing before industrial deployment.
AI-generated from the published abstract. Always read the original work before citing.
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.
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DOI: 10.29020/nybg.ejpam.v18i1.5712
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