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Pragmatical Asymptotical Stability Theorems on Partial Region and for Partial Variables with Applications to Gyroscopic Systems

Published online by Cambridge University Press:  05 May 2011

Zheng-Ming Ge  and
Jung-Kui Yu
Zheng-Ming Ge*
Affiliation:
Department of Mechanical Engineering, National Chiao Tung University, Hsinchu, Taiwan 30050, R.O.C.
Jung-Kui Yu*
Affiliation:
Engineer of Chung-Shan Institute of Science & Technology
*
*Professor
**Graduate student
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Abstract

For a long time, all stability theorems are concerned with the stability of the zero solution of the differential equations of disturbed motion on the whole region of the neighborhood of the origin. But for various problems of dynamical systems, the stability is actually on partial region. In other words, the traditional mathematical model is unmatched with the dynamical reality and artificially sets too strict demand which is unnecessary. Besides, although the stability for many problems of dynamical systems may not be mathematical asymptotical stability, it is actual asymptotical stability — namely “pragmatical asymptotical stability” which can be introduced by the concept of probability. In order to fill the gap between the traditional mathematical model and dynamical reality of various systems, one pragmatical asymptotical stability theorem on partial region and one pragmatical asymptotical stability theorem on partial region for partial variables are given and applications for gyroscope systems are presented.

Keywords

StabilityPartial regionPartial variablesPragmatical asymptotical stability
Type
Articles
Information
Journal of Mechanics , Volume 16 , Issue 4 , December 2000 , pp. 179 - 187
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2000

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