Speed Self-Stabilization

Abstract

The aim of the work is to find a mechanical analogue of cyclotron motion and to determine the scheme of the corresponding device, which is appropriate to call a stabilized rotator. From the key circumstance that determines the possibility of generalizing cyclotron motion to mechanics, which consists in the fact that the Lagrangian of an electron is twice as large as its kinetic energy, which, as applied to a stabilized rotator, should be interpreted as the equality of kinetic and potential energies, it follows that the composition of a stabilized rotator should include elements, which are able to store both of these types of energy, namely, the load and the spring. The natural frequency of rotation of a stabilized rotator is strictly fixed (it does not depend on either the moment of inertia or the moment of momentum) and remarkably coincides with the natural frequency of oscillations of a pendulum with identical parameters. When the angular momentum changes, the radius and tangential velocity change (the rotation frequency does not change and is equal to its own). The position of the load, in which its center of mass coincides with the axis of rotation, corresponds to a state of indefinite equilibrium. During rotation, the load can deviate with equal probability in any of the two directions and, accordingly, both compression and extension of the spring can develop. The state of indefinite equilibrium can be eliminated by providing the initial (static) displacement of the load and the initial deformation of the spring equal to it. Just as the frequency does not coincide with the natural frequency during forced oscillations of the pendulum, the rotation frequency of a stabilized rotator under loading does not coincide with the natural rotation frequency. At zero torque in the stationary mode, the rotational speed of the stabilized rotator cannot be arbitrary and takes on a single value. A stabilized rotator can be used to control the natural frequency of a radial oscillator, although in this capacity it may have strong competition from mechatronic systems. On the contrary, as a rotation stabilizer, its competitive capabilities are undeniable and are determined by the extreme simplicity of the design.