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

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 {Ii} (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 Ki = {Ii Ωi} (Ωi 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.