Rotator with constant speed

Abstract

The aim of the work is to find a mechanical analogue of cyclotron motion and to determine the scheme of the corresponding device to be appropriately called a stabilized rotator. The topic of speed stabilization is relevant. From the key circumstance determining the possibility of generalizing cyclotron motion to mechanics, consisting 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 a stabilized rotator should include elements, capable 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 angular 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 (while the rotation frequency does not change and is equal to the natural). At zero torque in the stationary mode, the rotational frequency of the stabilized rotator cannot be random and takes on a single value. Just as the forced oscillation frequency of the pendulum does not coincide with its natural frequency, the rotation frequency of a stabilized rotator under loading does not coincide with its natural rotation frequency. A stabilized rotator can be used to control the natural frequency of a radial oscillator, although in this case it may meet 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.