【摘要】 根据拉格朗日轴对称陀螺的运动学方程和三个守恒方程，建立了章动角的微分方程。引入三个无量纲的守恒参数，将章动角的微分方程无量纲化。利用章动角的守恒函数和守恒根，求出章动角的解析解和周期的解析解。推导了自转角速度和进动角速度的公式，提出了自转角和进动角的计算公式。根据初始条件计算了守恒参数，绘制了陀螺质心的运动轨迹。深入分析了过极点的轨迹和规则进动轨迹的初始条件之间的关系，说明了轨迹的类型。更多还原

【Abstract】 According to the kinematic equation of Lagrange axisymmetric gyroscope and three conservation equations, the differential equation of nutation angle is established. Three dimensionless conservative parameters are introduced to nondimensionlize the differential equation of nutation angle. Using the conservation function and conservation roots of the nutation angle, the analytic solution of the nutation angle and the periodic analytic solution are obtained. The formulas for the rotation angular velocity and precession angular velocity are derived, and the calculation formulas for the rotation angle and precession angle are proposed. The conservation parameters are calculated according to the initial conditions, and the trajectory of the center of mass of the gyro is drawn. The relationship between the trajectory of the crossing pole and the initial conditions of the regular precession trajectory is deeply analyzed, and the type of trajectory is explained.更多还原