treams.special.vsph2cyl

treams.special.vsph2cyl(v, r) = <ufunc 'vsph2cyl'>

Convert vector in spherical coordinates to vector in cylindrical coordinates

The spherical vector \((v_r, v_\theta, v_\varphi)\) at coordinates \((r, \theta, \varphi)\) is converted to \((v_\rho, v_\varphi, v_z)\) with

\[\begin{split}\begin{pmatrix} v_\rho \\ v_\varphi \\ v_z \end{pmatrix} = \begin{pmatrix} \sin \theta & \cos \theta & 0 \\ 0 & 0 & 1 \\ \cos \theta & -\sin \theta & 0 \end{pmatrix} \begin{pmatrix} v_r \\ v_\theta \\ v_\varphi \end{pmatrix}\end{split}\]

Parameters:

• v (float or complex, 3-array) – Vector in 3-dimensional spherical space

• r (float, 3-array) – Spherical coordinates in 3-dimensional space

Returns:

float or complex, 3-array