Quasi-stationary finite control of the motion of hybrid oscillatory systems

The uniaxial (translational or rotational) motions of a mechanical system containing absolutely rigid bodies (material points or flywheels) are investigated analytically. The system components are connected in series by elastic elements with distributed characteristics (springs, beams, or shafts). It is assumed that concentrated control action (forces or moments) is applied to the rigid bodies or to the ends of the elastic links. The approach adopted here is based on the concept of the quasi-stationary nature of forced elastic deviations in the presence of sufficiently smooth control action.