6. Apéndice - Transformación de Coordenadas


Transformación de coordenadas
Rectangular a cilíndrica:
\begin{array}{c|ccc} & \hat{x} & \hat{y} & \hat{z}\\\hline\hat{\rho} & \cos\phi & \sin\phi & 0 \\\hat{\phi} & -\sin\phi & \cos\phi & 0 \\\hat{z} & 0 & 0 & 1 \\\end{array}

Rectangular a esférica:
\begin{array}{c|ccc} & \hat{x} & \hat{y} & \hat{z} \\\hline\hat{r} & \sin\theta \cos\phi & \sin\theta \sin\phi & \cos\theta \\\hat{\theta} & \cos\theta \cos\phi & \cos\theta \sin\phi & -\sin\theta \\\hat{\phi} & -\sin\phi & \cos\phi & 0 \\\end{array}

Cilíndrica a rectangular:

\begin{array}{c|ccc} & \hat{\rho} & \hat{\phi} & \hat{z} \\\hline\hat{x} & \cos\phi & -\sin\phi & 0 \\\hat{y} & \sin\phi & \cos\phi & 0 \\\hat{z} & 0 & 0 & 1 \\\end{array}

Cilíndrica a esférica:

\begin{array}{c|ccc} & \hat{\rho} & \hat{\phi} & \hat{z} \\\hline\hat{r} & \sin\theta & 0 & \cos\theta \\\hat{\theta} & \cos\theta & 0 & -\sin\theta \\\hat{\phi} & 0 & 1 & 0 \\\end{array}


Esférica a rectangular:
\begin{array}{c|ccc} & \hat{r} & \hat{\theta} & \hat{\phi} \\\hline\hat{x} & \sin\theta \cos\phi & \cos\theta \cos\phi & -\sin\phi \\\hat{y} & \sin\theta \sin\phi & \cos\theta \sin\phi & \cos\phi \\\hat{z} & \cos\theta & -\sin\theta & 0 \\\end{array}

Esférica a cilíndrica:

\begin{array}{c|ccc} & \hat{r} & \hat{\theta} & \hat{\phi} \\\hline\hat{\rho} & \sin\theta & \cos\theta & 0 \\\hat{\phi} & 0 & 0 & 1 \\\hat{z} & \cos\theta & -\sin\theta & 0 \\\end{array}


Coordenadas