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.

This paper deals with the numerical solution of option pricing stochastic volatility model described by a time-dependent, two-dimensional convection-diffusion reaction equation. Firstly, the mixed spatial derivative of the partial differential equation (PDE) is removed by means of the classical technique for reduction of second-order linear partial differential equations to canonical form. An explicit difference scheme with positive coefficients and only five-point computational stencil is constructed. The boundary conditions are adapted to the boundaries of the rhomboid transformed numerical domain. Consistency of the scheme with the PDE is shown and stepsize discretization conditions in order to guarantee stability are established. Illustrative numerical examples are included.

The aim of this study is to explore the static and dynamic performance characteristics of finite journal bearings lubricated with a non-Newtonian ferrofluid in the presence of an external magnetic field using the spectral method technique. The modified Reynolds equation governing the film pressure, coming out from the combination of the momentum and continuity equations, is derived. We use the pressure distribution function to study the static and dynamic characteristics and the stability of the given system. Numerical applications are achieved in order to investigate the influence of the various parameters on the stability behavior of the system. For instance, it is observed that the journal loci get stable as the magnetic force increases. The non-Newtonian, the distance ratio, and the magnetic parameters play an important role in administrating the stability behavior. The non-Newtonian parameter is found to stabilize the system, while the magnetic force coefficient destabilizes it. Furthermore, for law eccentricity ratios, the stability of this system is significant.