On the decoupling and the solutions of the Euler dynamic equations governing the motion of a gyroscope
Abstract
The decoupling and the solutions of the three strongly nonlinear ordinary dynamic differential equations, governing the motion of an arbitrary rigid body, free to rotate about a fixed point (gyro) are presented. The theory developed is based on the assumption that the instantaneous angular velocity and the momentcomponents are arbitrary smooth functions of the time. By a quantitative analysis, analytical solutions of the resulting differential equations were obtained under some general conditions in accordance with the physical problem. Finally, a theoretical application is investigated concerning the dynamic response of a oneaxis symmetrical gyroscope subjected to an arbitrary external loading.
 Publication:

Zeitschrift Angewandte Mathematik und Mechanik
 Pub Date:
 1990
 DOI:
 10.1002/zamm.19900701103
 Bibcode:
 1990ZaMM...70..489P
 Keywords:

 Decoupling;
 Differential Equations;
 Dynamical Systems;
 Euler Equations Of Motion;
 Gyroscopic Stability;
 Angular Velocity;
 Dynamic Response;
 Loads (Forces);
 Rigid Structures;
 Physics (General)