Modeling of the optimal deceleration for the rotatory motion of asymmetric rigid body

Abstract

This paper investigates a minimum time of the 3D slowing rotatory motion of free asymmetric rigid body under the influence of a rotatory moment of viscous friction and a gyrostatic one. It is considered that the body center of mass coincides with the origin point of two Cartesian frames. The law of optimal control for the slow body’s rotation is formulated, and the associated time and phase paths are evaluated. The achieved novel results are obtained and plotted for two new cases in some graphical representations to detect the good effects of the gyrostatic moment. The comparison between our results and the previous one shows great consistency between them in the absence of influence of the gyrostatic moment, in which the differences between them are discussed. Therefore, the attained results generalized those which were obtained in previous works. The relevance of this work is due to its practical applications, especially for the gyroscopic theory applications in maintaining stability and determining the ordination of aircraft and submarine vehicles.