On the basis of analyzing the rolling walking of spherical robot , this paper derived the condition of taking off , obtained the differential equation of jumping movement of spherical robot by the use of lagrange equation , and gained the formulae of jumping height and jumping length of spherical robot by means of solving the differential equation of this jumping movement 在分析球形机器人滚动行走的基础上，推导出了球形机器人的起跳条件；利用拉格朗日方程得到了球形机器人跳跃运动微分方程；通过求解该跳跃运动微分方程得到了球形机器人跳跃高度和跳跃长度的公式。
Firstly , in order to treat the local weakened effect of the crack on the shaft , the equivalent line - spring model is built . then the constitutive equations are derived and the flexibility model of the rotating shaft is discussed . based on the lagrange equations , the non - linear dimensionless differential equations of the single rotor system with the disk and crack located at an arbitrary position of the shaft are obtained 首先为处理裂纹对轴的局部削弱作用，提出了等效线弹簧模型，推导了线弹簧弹性本构关系，获得了裂纹转动轴的柔度模型，然后，应用lagrange方程建立了盘和裂纹处于轴任意位置的无量纲的单盘转子系统的非线性运动控制微分方程。
Setup of experimental system and experiment research first , coupling characteristic between flexible appendages and central rigid body is theoretically analyzed . based on simplifying the object studied , its theoretical model is derived by applying lagrange equation , and the coupling characteristic is analyzed . the control modals of flexible appendages are determined through calculating rolling couple coefficient and simulation of real coupling structure 将研究对象简化为带有对称柔性梁的刚性体，分析了柔性附件与中心刚体的运动耦合模式，并对影响中心刚体姿态角的反对称耦合模式建立了动力学方程，通过对实际结构转动耦合系数的计算和仿真分析，确定了柔性附件振动控制的重点模态。
