treams.special.vcyl2sph

treams.special.vcyl2sph(v, r) = <ufunc 'vcyl2sph'>

Convert vector in cylindrical coordinates to vector in spherical coordinates

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

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

Parameters:

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

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

Returns:

float or complex, 3-array