兩個不穩定性定理及其對自由陀螺穩定性的應用

Abstract

本篇論文提出兩個不同於傳統N. G. Chetaeff不穩定性定理的兩個 新定理(各自對自治及非自治系統)，藉由檢驗V函數的高次導數，來 判別系統的不穩定性。經由本理論之第一個定理，自由陀螺儀因框架 質量所造成的漂移現象能夠得到證明，此外，並提出一些二階微分方 程作為本理論的應用實例。

Two theorems of instability, different from the traditional Cheataeffs instability theorem are developed. The theorems determine instability of autonomous and non-autonomous dynamical systems by means of investigating the higher-order derivatives of the Lyapunov function. Using the first theorem of these theorems, the walk of a free gyroscope which is caused by the mass of the gimbals can be proven. Furthermore, several second-order differential equations are presented as the applications of these two theorems.