判别函数定号性和变号性的几个定理及其对睡陀螺轴运动条件稳定性的应用

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Some Theorems for Determining the Definiteness and Changeability of Sign of Functions and the Application to the Conditional Stability of the Motion of the Axis of a Sleeping Top

Teaching and Research Section of General Mechanics, Department of Engineering Mechanics, Shanghai Chiao-Tung University, Shanghai

摘要: 本文给出判别函数定号性和变号性的几个定理并给出其对睡陀螺轴运动条件稳定性的应用.从而得出睡陀螺轴运动条件稳定的必充条件.它与章动角稳定和运动方程全部变量稳定的必充条件吻合.

Abstract: This paper gives some theorems for determining the definiteness and changeability of sign of functions as well as the application to the axis of a sleeping top. The necessary and sufficient condition of the conditional stability of the motion is obtained, which coincides with that of the stability of nutation angle and also with that of the stability of total variables in the equations of motion.