本文建立拉格朗日陀螺运动方程的解析方法．导出拉格朗日陀螺做规则进动的条件，用级数展开技术得到规则进动附近的小角度章动和进动的解析解．给出陀螺自转轴运动的简明图像，即重力引起绕竖直轴的规则进动和无重力的自由进动的叠加．利用解析结果对陀螺不倒之谜给出解释.

In this paper，the analytical method of Lagrange gyroscope motion equation is established．The condition for regular precession of Lagrange gyroscope is derived，and the analytical solution for nutation with small angle and precession near regular precession is obtained by series expansion technique．A concise picture of the gyroscope rotation axis motion is given，that is，the superposition of the regular precession around the vertical axis caused by gravity and the free precession without gravity. According to the analytical solution，the mystery of the gyroscope not falling down is explained.