Mathematical Models for the Top Motions and Gyroscope Nutation

Abstract

All rotating objects of different designs and functions in engineering manifest gyroscopic effects that should be mathematically described and explained by physical principles. The action of the inertial torques on the simple top and the gyroscope of the complex design is the same and manifested by complex motions that researchers could not describe exactly for the long time. The new mathematical models for the system interrelated inertial torques acting on the spinning objects are enabled for describing the gyroscopic effects and related their motions. The analytical approach for a top and gyroscope nutation is considered by the action of the interrelated inertial torques of the spinning objects and by the principle of potential and kinetic energy conservation law. This dual approach is compulsory and enables to solve all gyroscope problems for all rotating objects and gyroscopic devices in engineering.