Modelling and analysis of a gyrostat elastically attached to a vehicle

In recent studies, the dynamic response of a passenger car to a gyrostat was investigated for a series of driving manoeuvres, but the gyrostat was assumed to be rigidly supported, thus neglecting the effect of rotor precession. The aim of the present study is the modelling and investigation of the gyrostat-vehicle interaction for elastically mounted gyrostats. For this purpose, a general model describing the motion of a gyrostat elastically supported by a moving platform is derived. Emphasis is placed on the mathematical derivation, where all considerations that are necessary to arrive at the final result are included. Thus, the presented considerations and results can be easily adopted and are suitable to serve beyond their actual purpose as a reference work for other applications. The derived model is tested with the aid of vehicle dynamics simulations and the simulation results prove to be consistent with the results of the rigid attachment model, provided that the elastic approach is subjected to high-bearing stiffnesses. However, it is shown that at lower bearing stiffnesses the solutions are progressively different, since low-bearing stiffnesses enable the gyrostat to move, due to the compliance of the bearings itself, relative to the vehicle chassis with high-angular velocities.