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On the Decoupling and the Solutions of the Euler Dynamic Equations Governing the Motion of a Gyroscope
Author(s) -
Panayotounakos D. E.,
Theocaris P. S.
Publication year - 1990
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19900701103
Subject(s) - decoupling (probability) , gyroscope , nonlinear system , angular velocity , rigid body , equations of motion , euler's formula , ordinary differential equation , classical mechanics , physics , rigid body dynamics , differential equation , euler equations , mathematical analysis , dynamic equation , mathematics , control theory (sociology) , computer science , quantum mechanics , control engineering , engineering , control (management) , artificial intelligence
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 moment‐components 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 one‐axis symmetrical gyroscope subjected to an arbitrary external loading.