Mathematical models for gyroscope properties

Abstract

Gyroscope devices are primary units for navigation and control systems that have a wide application in aerospace and other industries. The main property of the gyroscope device is maintaining the axis of a spinning rotor. This gyroscope peculiarity is represented in terms of gyroscope effects in which mathematical models have been formulated on the law of kinetic energy conservation and changes in angular momentum. However, the origin of gyroscope effects is more complex and known mathematical models do not match the actual forces and motions in these devices. Recent investigations in this area have demonstrated that, in a gyroscope are acting simultaneously and interdependently centrifugal, common inertial and Coriolis forces as well as changes the change in the angular momentum. These forces are results of external torque applied to the gyroscope that generates internal resistance and precession torques, which manifest several gyroscope properties. In engineering area, the gyroscopic devices can be loaded by several external torques acting around axes. Each external torque generates the internal resistance and precession torques acting around two axes. The
action of external torques applied to the gyroscope with one side support demonstrates its turn up, which is the result of action of the internal inertial torques. The manifestation of these gyroscope properties depends on which axes are applied external torques. This paper represents mathematical models for the gyroscope motions around two axes and properties based on the action of the two external torques applied to the gyroscope with one side support.