Journal of Mechanics


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

Zheng-Ming Gea1 c1 and Jung-Kui Yua2 c2

a1 Department of Mechanical Engineering, National Chiao Tung University, Hsinchu, Taiwan 30050, R.O.C.

a2 Engineer of Chung-Shan Institute of Science & Technology


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.

(Received February 29 2000)

(Revised August 25 2000)

(Accepted September 15 2000)


  • Stability;
  • Partial region;
  • Partial variables;
  • Pragmatical asymptotical stability


c1 Professor

c2 Graduate student