オイラー角 計算ツール (Euler Angle Calculator)

軸の方向 (Orientation)
軸の順番 (Order)
オイラー角 (Euler Angles)

°

°

°

記号 (Symbols)
回転軸回転角度基底変換
zzα=0.0°\alpha = 0.0°(x′,y′,z′)=(x,y,z)Rz(α)(\bm{x'}, \bm{y'}, \bm{z'}) = (\bm{x}, \bm{y}, \bm{z}) R_z(\alpha)
回転軸回転角度基底変換
y′y'β=0.0°\beta = 0.0°(x′′,y′′,z′′)=(x′,y′,z′)Ry(β)(\bm{x''}, \bm{y''}, \bm{z''}) = (\bm{x'}, \bm{y'}, \bm{z'}) R_y(\beta)
回転軸回転角度基底変換
x′′x''γ=0.0°\gamma = 0.0°(X,Y,Z)=(x′′,y′′,z′′)Rx(γ)(\bm{X}, \bm{Y}, \bm{Z}) = (\bm{x''}, \bm{y''}, \bm{z''}) R_x(\gamma)
(x,y,z)=((1,0,0)T,(0,1,0)T,(0,0,1)T)(α,β,γ)=(0°,0°,0°)(X,Y,Z)=(x,y,z)Rx(α)Ry(β)Rz(γ)=(x,y,z)(cos⁡α−sin⁡α0sin⁡αcos⁡α0001)(cos⁡β0sin⁡β010−sin⁡β0cos⁡β)(1000cos⁡γ−sin⁡γ0sin⁡γcos⁡γ)=(cos⁡αcos⁡β−sin⁡αcos⁡γ+sin⁡βsin⁡γcos⁡αsin⁡αsin⁡γ+sin⁡βcos⁡αcos⁡γsin⁡αcos⁡βsin⁡αsin⁡βsin⁡γ+cos⁡αcos⁡γsin⁡αsin⁡βcos⁡γ−sin⁡γcos⁡α−sin⁡βsin⁡γcos⁡βcos⁡βcos⁡γ)=(1.00000000.00000000.00000000.00000001.00000000.00000000.00000000.00000001.0000000) \begin{align*} (\bm{x}, \bm{y}, \bm{z}) &= ((1, 0, 0)^T, (0, 1, 0)^T, (0, 0, 1)^T) \\ (\alpha, \beta, \gamma) &= (0°, 0°, 0°) \\ (\bm{X}, \bm{Y}, \bm{Z}) &= (\bm{x}, \bm{y}, \bm{z}) R_x(\alpha) R_y(\beta) R_z(\gamma) \\ &= (\bm{x}, \bm{y}, \bm{z}) \begin{pmatrix} \cos \alpha & -\sin \alpha & 0 \\ \sin \alpha & \cos \alpha & 0 \\ 0 & 0 & 1 \\ \end{pmatrix}\begin{pmatrix} \cos \beta & 0 & \sin \beta \\ 0 & 1 & 0 \\ -\sin \beta & 0 & \cos \beta \\ \end{pmatrix}\begin{pmatrix} 1 & 0 & 0 \\ 0 & \cos \gamma & -\sin \gamma \\ 0 & \sin \gamma & \cos \gamma \\ \end{pmatrix} \\ &= \begin{pmatrix} \cos \alpha \cos \beta & -\sin \alpha \cos \gamma + \sin \beta \sin \gamma \cos \alpha & \sin \alpha \sin \gamma + \sin \beta \cos \alpha \cos \gamma \\ \sin \alpha \cos \beta & \sin \alpha \sin \beta \sin \gamma + \cos \alpha \cos \gamma & \sin \alpha \sin \beta \cos \gamma -\sin \gamma \cos \alpha \\ -\sin \beta & \sin \gamma \cos \beta & \cos \beta \cos \gamma \end{pmatrix} \\ &= \begin{pmatrix} 1.0000000 & 0.0000000 & 0.0000000 \\ 0.0000000 & 1.0000000 & 0.0000000 \\ 0.0000000 & 0.0000000 & 1.0000000 \end{pmatrix} \end{align*}