Mathematical models for inertial torques acting on a spinning ring

Since the Industrial Revolution, researchers paid attention to the remarkable gyroscope properties of gyroscopic devices and tried to develop the gyroscope theory. The simplified theories of gyroscopes started to publish a hundred years ago.1–4 numerous publications described gyroscopic effects and applications in engineering but none of them explained the physics of gyroscope properties.5–7 the action of the gyroscopic effects is an important aspect of the science of classical mechanics. Fundamental textbooks and manuals have chapters of gyroscope theory.8,9 Many simplified approaches to gyroscope theory are dedicated to gyroscopic effects.10,11 All publications based on assumptions and described gyroscopic effects in terms only of the angular momentum.12–14 Researchers focused attention on the action of inertial forces on the gyroscope but did not represent mathematical models.15,16 The known theories of gyroscopic effects do not adequate to actual motions of rotating objects.17,18 Unsolved gyroscopic problems generated artificial terms as gyroscope resistance, gyroscopic effects and attributed fantastical properties to rotating objects.19,20 Still, gyroscopic effects attract researchers to find true theory.21,22 New investigations in the area of gyroscope theory discovered the action of the system of inertial torques on rotating objects. This work describes the application of new mathematical models for the system of inertial torques generated by the rotating mass of the spinning ring.