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以欧拉参数为广义坐标（准坐标），相对角速度和相对移动速度为广义速率，采用Ｋａｎｅ方程的Ｈｕｓｔｏｎ 形式建立多体系统的运动力学方程。由伪上三角分解求约束Ｊａｃｏｂｉ矩阵的正交补阵，约简约束力，从而将运动方程由微分几何方程（ＤＡＥ）变为常微分方程（ＯＤＥ），并由Ｇｅａｒ 法对ＯＤＥ积分求出运动历程。最后给出一伸展臂数值分析算例。
Taking Euler parameters as generalized coordinates (quasi-coordinates), relative angular velocity and relative moving velocity as generalized velocity, the kinematic equation of multi-body system is established by Huston’s form of Kane’s equation. The orthogonal complement of constrained Jacobian matrices is reduced by pseudo-upper triangular decomposition to reduce the binding force, which changes the equation of motion from differential geometry equation (DAE) to ordinary differential equation (ODE) and obtains the ODE integral by Gear method course. Finally, a numerical example of stretching arm is given.