Inertial torques acting on a spinning paraboloid

Numerous gyroscopic devices consist of rotating components that manifest gyroscopic effects, i.e., the action of unexplainable inertial torques. The rotating objects in engineering can be designed as a disk, cylinder, rotor, circular cone, sphere, paraboloid, etc. Known theories express gyroscopic effects by a simplified mathematical model based only on the principle of the change in the angular momentum for the spinning disk. New research in the area of the gyroscope theory has shown that the physics of inertial torques is more complex than that presented in known publications. Spinning objects generate a system of interrelated inertial torques based on the action of centrifugal, common inertial, and Coriolis forces, as well as the change in the angular momentum. The action of inertial torques manifests resistance and precession torques, which is known as gyroscopic effects. These inertial torques constitute the fundamental principles of the gyroscope theory. The rotating objects of complex designs demonstrate the action of inertial torques, in which mathematical models are different from the models of the spinning disk. The novelty of the work is analytical solutions for the inertial torques generated by the rotating mass of the spinning paraboloid that is new in the dynamics of rotating objects.