Controlled motion modes of a gyroscopic pendulum in a gimbal suspension

The issues of controlling the motion of a gyroscopic pendulum fixed in a gimbal suspension and having three degrees of freedom are discussed in the paper. It is proposed to use physical analogies and correlate their action with the dissipative forces of external viscous friction, friction in gimbal joints and internal friction in the pendulum rod, as well as inertial forces and gyroscopic forces to form the control torques in gimbal joints. Six modes of controlled movement of the system are considered, which allow achieving various goals. It is shown that it is possible to completely suppress the motions of a gyroscopic pendulum, switch it to the mode of a spherical or physical pendulum, enter the mode of rotation around a fixed vertical axis, bring it to the mode of regular precession, and also strengthen or weaken the gyroscopic structure of the motion equations. The discussion of these modes of controlled motion is accompanied by the construction of motion equations both within the framework of the original nonlinear model and for simplified linear or weakly nonlinear models. The obtained results are theoretically interesting and may be useful for specific practical applications in the field of gyroscopic technology.