Modeling the Optimum Deceleration for the Motion of Asymmetric Rigid Body

Abstract

Abstract Purpose In this study, we investigate the minimum time (MT) for the spatial motion of a free rigid body (RB) under the influence of viscous friction and gyrostatic moments (GMs). Assuming that the body’s center of mass coinciding with the original point of two Cartesian systems of coordinates. Results The optimal control (OC) law for the slow movements, as a main goal, is established, and the corresponding time and phase pathways are assessed. Conclusion The resulting innovative outcomes are achieved and displayed for two new scenarios in various graphs to show the gyrostatic moment’s positive impacts. When comparing the obtained results with the previous one when the gyrostatic moment isn’t present, amazing consistency is observed, and the slight deviations between them are discussed. As a result, the acquired results generalize those that were discovered in earlier investigations. Applications The significance of this study arises from its practical implications in everyday existence, that confine themself to applying gyroscopic theory to preserve the stability and balance of vehicles in the design of which gyroscopes are used, in addition to determining the path of aircraft and marine vehicles.