坐标系转动的4种数学表示方式

(1)(等效旋转矢量)$\varphi =w+\frac{1}{2}\varphi \times w+\frac{1}{{\theta }^2}(1-\frac{\theta }{2}cot\frac{\theta }{2})(\varphi {)}^{2}w$ (2)(4元数)$q=cos\frac{\theta }{2}+usin\frac{\theta }{2}$ (3)(旋转矩阵)$q=\frac{1}{2}q。w$ (4)(旋转矩阵)$C=I+2q_0(q_v\times )+2(q_v\times {)}^2$ (5)(旋转矩阵)$C=Cw\times$ 补充:q->w $w=u\dot{\varphi }+\dot{u}sin\theta +\dot{u}\times u(1-cos\theta )$