History and Present of Gyroscope Models and Vector Rotators

 

Ljiljana Veljović

 

The objective of this paper is to give a short historical overview of models and constructions of gyroscopes and present models as well as their component motions. All mechanical gyroscopes are based on coupled rotations around more axes with one point of intersection.

Therefore, this paper contains two related parts. The first part presents the kinetic parameters of the rigid body rotations around two axes without intersection when the rigid body is skew and eccentrically positioned to the spin axis.

In addition, the paper presents some of the original results in the area of nonlinear dynamics of gyro rotors applicable in the explanation of some nonlinear phenomena in gyroscope dynamics, obtained by Hedrih and Veljovic. Hedrih’s mass moment vectors and vector rotators are used to present some characteristic members of vector expressions in the linear momentum and the angular momentum and their derivatives for the gyro rotor rotation around two axes without intersection. The paper also gives a graphical presentation of the phase portrait and the kinematical vector rotator for different normal distances between the axes and the skew position of the axes. Imprecision and errors in the function of gyroscopes are caused by eccentricity and unbalance of gyro rotors as well by the distance between the rotation axes. The given graphs are thus important for the explanation and necessary corrections of the gyroscope functioning.

In the second part, the paper presents an overview of the history and the present of gyroscope models and their construction realizations used to manage and stabilize the movement of ships, aircraft, vehicles and torpedoes. With the development of micro and nano technology, a new class of gyroscopes emerges.

Key words: gyroscope, gyro stabilizer, gyrocompass, gyroscope rotor, gyro-stabilized platform, inertial platform, rotator, momentum, angular momentum, vector analysis.