欧拉角转四元数转换公式_1.04+0.4*cosw怎么变成

欧拉角对应关系：

$\large X-\alpha ,Y-\beta ,Z-\gamma$

X-Y-Z：

$\large q=\begin{bmatrix}cos\frac{\gamma }{2} \\ 0 \\ 0 \\ sin\frac{\gamma }{2} \end{bmatrix}\begin{bmatrix}cos\frac{\beta }{2} \\ 0 \\ sin\frac{\beta }{2} \\ 0 \end{bmatrix}\begin{bmatrix}cos\frac{\alpha }{2} \\ sin\frac{\alpha }{2} \\ 0 \\ 0 \end{bmatrix}=\begin{bmatrix}cos\frac{\alpha }{2}cos\frac{\beta}{2}cos\frac{\gamma }{2}+sin\frac{\alpha }{2}sin\frac{\beta}{2}sin\frac{\gamma }{2} \\ sin\frac{\alpha }{2}cos\frac{\beta }{2}cos\frac{\gamma }{2}-cos\frac{\alpha }{2}sin\frac{\beta }{2}sin\frac{\gamma }{2} \\ cos\frac{\alpha }{2}sin\frac{\beta }{2}cos\frac{\gamma }{2}+sin\frac{\alpha }{2}cos\frac{\beta }{2}sin\frac{\gamma }{2} \\ cos\frac{\alpha }{2}cos\frac{\beta }{2}sin\frac{\gamma }{2}-sin\frac{\alpha }{2}sin\frac{\beta }{2}cos\frac{\gamma }{2} \end{bmatrix}$

X-Z-Y：

$\large q=\begin{bmatrix}cos\frac{\beta }{2} \\ 0 \\ sin\frac{\beta }{2} \\ 0 \end{bmatrix}\begin{bmatrix}cos\frac{\gamma }{2} \\ 0 \\ 0 \\ sin\frac{\gamma }{2} \end{bmatrix}\begin{bmatrix}cos\frac{\alpha }{2} \\ sin\frac{\alpha }{2} \\ 0 \\ 0 \end{bmatrix}=\begin{bmatrix}cos\frac{\alpha }{2}cos\frac{\beta}{2}cos\frac{\gamma }{2}-sin\frac{\alpha }{2}sin\frac{\beta}{2}sin\frac{\gamma }{2} \\ sin\frac{\alpha }{2}cos\frac{\beta }{2}cos\frac{\gamma }{2}+cos\frac{\alpha }{2}sin\frac{\beta }{2}sin\frac{\gamma }{2} \\ cos\frac{\alpha }{2}sin\frac{\beta }{2}cos\frac{\gamma }{2}+sin\frac{\alpha }{2}cos\frac{\beta }{2}sin\frac{\gamma }{2} \\ cos\frac{\alpha }{2}cos\frac{\beta }{2}sin\frac{\gamma }{2}-sin\frac{\alpha }{2}sin\frac{\beta }{2}cos\frac{\gamma }{2} \end{bmatrix}$

Y-X-Z：

$\large q=\begin{bmatrix}cos\frac{\gamma }{2} \\ 0 \\ 0 \\ sin\frac{\gamma }{2} \end{bmatrix}\begin{bmatrix}cos\frac{\alpha }{2} \\ sin\frac{\alpha }{2} \\ 0 \\ 0 \end{bmatrix}\begin{bmatrix}cos\frac{\beta }{2} \\ 0 \\ sin\frac{\beta }{2} \\ 0 \end{bmatrix}=\begin{bmatrix}cos\frac{\alpha }{2}cos\frac{\beta}{2}cos\frac{\gamma }{2}-sin\frac{\alpha }{2}sin\frac{\beta}{2}sin\frac{\gamma }{2} \\ sin\frac{\alpha }{2}cos\frac{\beta }{2}cos\frac{\gamma }{2}-cos\frac{\alpha }{2}sin\frac{\beta }{2}sin\frac{\gamma }{2} \\ cos\frac{\alpha }{2}sin\frac{\beta }{2}cos\frac{\gamma }{2}+sin\frac{\alpha }{2}cos\frac{\beta }{2}sin\frac{\gamma }{2} \\ cos\frac{\alpha }{2}cos\frac{\beta }{2}sin\frac{\gamma }{2}+sin\frac{\alpha }{2}sin\frac{\beta }{2}cos\frac{\gamma }{2} \end{bmatrix}$

Y-Z-X：

$\large q=\begin{bmatrix}cos\frac{\alpha }{2} \\ sin\frac{\alpha }{2} \\ 0 \\ 0 \end{bmatrix}\begin{bmatrix}cos\frac{\gamma }{2} \\ 0 \\ 0 \\ sin\frac{\gamma }{2} \end{bmatrix}\begin{bmatrix}cos\frac{\beta }{2} \\ 0 \\ sin\frac{\beta }{2} \\ 0 \end{bmatrix}=\begin{bmatrix}cos\frac{\alpha }{2}cos\frac{\beta}{2}cos\frac{\gamma }{2}+sin\frac{\alpha }{2}sin\frac{\beta}{2}sin\frac{\gamma }{2} \\ sin\frac{\alpha }{2}cos\frac{\beta }{2}cos\frac{\gamma }{2}-cos\frac{\alpha }{2}sin\frac{\beta }{2}sin\frac{\gamma }{2} \\ cos\frac{\alpha }{2}sin\frac{\beta }{2}cos\frac{\gamma }{2}-sin\frac{\alpha }{2}cos\frac{\beta }{2}sin\frac{\gamma }{2} \\ cos\frac{\alpha }{2}cos\frac{\beta }{2}sin\frac{\gamma }{2}+sin\frac{\alpha }{2}sin\frac{\beta }{2}cos\frac{\gamma }{2} \end{bmatrix}$

Z-X-Y：

$\large q=\begin{bmatrix}cos\frac{\beta }{2} \\ 0 \\ sin\frac{\beta }{2} \\ 0 \end{bmatrix}\begin{bmatrix}cos\frac{\alpha }{2} \\ sin\frac{\alpha }{2} \\ 0 \\ 0 \end{bmatrix}\begin{bmatrix}cos\frac{\gamma }{2} \\ 0 \\ 0 \\ sin\frac{\gamma }{2} \end{bmatrix}=\begin{bmatrix}cos\frac{\alpha }{2}cos\frac{\beta}{2}cos\frac{\gamma }{2}+sin\frac{\alpha }{2}sin\frac{\beta}{2}sin\frac{\gamma }{2} \\ sin\frac{\alpha }{2}cos\frac{\beta }{2}cos\frac{\gamma }{2}+cos\frac{\alpha }{2}sin\frac{\beta }{2}sin\frac{\gamma }{2} \\ cos\frac{\alpha }{2}sin\frac{\beta }{2}cos\frac{\gamma }{2}-sin\frac{\alpha }{2}cos\frac{\beta }{2}sin\frac{\gamma }{2} \\ cos\frac{\alpha }{2}cos\frac{\beta }{2}sin\frac{\gamma }{2}-sin\frac{\alpha }{2}sin\frac{\beta }{2}cos\frac{\gamma }{2} \end{bmatrix}$

Z-Y-X：

$\large q=\begin{bmatrix}cos\frac{\alpha }{2} \\ sin\frac{\alpha }{2} \\ 0 \\ 0 \end{bmatrix}\begin{bmatrix}cos\frac{\beta }{2} \\ 0 \\ sin\frac{\beta }{2} \\ 0 \end{bmatrix}\begin{bmatrix}cos\frac{\gamma }{2} \\ 0 \\ 0 \\ sin\frac{\gamma }{2} \end{bmatrix}=\begin{bmatrix}cos\frac{\alpha }{2}cos\frac{\beta}{2}cos\frac{\gamma }{2}-sin\frac{\alpha }{2}sin\frac{\beta}{2}sin\frac{\gamma }{2} \\ sin\frac{\alpha }{2}cos\frac{\beta }{2}cos\frac{\gamma }{2}+cos\frac{\alpha }{2}sin\frac{\beta }{2}sin\frac{\gamma }{2} \\ cos\frac{\alpha }{2}sin\frac{\beta }{2}cos\frac{\gamma }{2}-sin\frac{\alpha }{2}cos\frac{\beta }{2}sin\frac{\gamma }{2} \\ cos\frac{\alpha }{2}cos\frac{\beta }{2}sin\frac{\gamma }{2}+sin\frac{\alpha }{2}sin\frac{\beta }{2}cos\frac{\gamma }{2} \end{bmatrix}$