Revisiting Euler-Poisson Equations for a Rigid Body under the Influence of Time-Dependent Temperature Field

Ershkov, Sergey V.

doi:10.22055/jacm.2024.47961.4873

Revisiting Euler-Poisson Equations for a Rigid Body under the Influence of Time-Dependent Temperature Field

Document Type : Research Paper

Author

Sergey V. Ershkov ¹ ^{, 2} ^{, 3}

¹ Sternberg Astronomical Institute, M.V. Lomonosov's Moscow State University, 13 Universitetskij prospect, Moscow 119992, Russian Federation

² Plekhanov Russian University of Economics, Scopus number 60030998, Stremyanny lane, 36, Moscow, 115054, Russian Federation

³ Russian Technological University (MIREA), 78 Vernadsky Avenue, Moscow 119454, Russian Federation

10.22055/jacm.2024.47961.4873

Abstract

In this illuminating research, the classical Euler-Poisson equations (describing the dynamics of rigid body rotations over the fixed point) have been revisited for the case of a rigid body that is under the influence of a time-dependent temperature field. It is shown that two classical first integrals of motion remain the same whereas the integral of energy should be updated accordingly to slowly variable principal moments of inertia {I_i} (i = 1, 2, 3) stemming from the temperature-dependent sizes of a rigid body. The revisited Euler-Poisson equations are reduced to the system of 3 nonlinear ordinary differential equations of 1-st order in regard to 3 functions K_i = {I_i Ω_i} (Ω_i are the components of angular velocity along the principal axes) for which the elegant approximate semi-analytical solutions have been obtained with numerical findings supported by graphical plots. Such theoretical findings can be useful in taking into account the stabilization of gyroscopes supporting the system of orientations of spacecraft on orbits since regimes of drastically changing temperature for technical equipment do exist in outer space.

Keywords

Euler-Poisson equations

rotations over the fixed point

rigid body dynamics

variable principal moments of inertia

temperature-dependent sizes of a rigid body

gyroscopes in spacecraft

Subjects

Computational Mechanics

Publisher’s Note Shahid Chamran University of Ahvaz remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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