F105 Rotate a Three-Dimensional Polar Coordinate System

POLROT calculates the values of $\theta \text{'}$ and $\phi \text{'}$ of the coordinate system $S\text{'}(\theta \text{'},\phi \text{'},r)$ , obtained by rotation of the 3-dimensional polar coordinate system $S(\theta ,\phi ,r)$ about any axis $(0\le \theta \le \pi ,0\le \phi \le 2\pi )$ .

Structure:

SUBROUTINE subprogram
User Entry Names: POLROT

Usage:

    CALL POLROT(THETA,PHI,THPRIM,PHPRIM,THAX,PHAX,ROTANG)

THETA

( REAL) Angle $\theta$ in the old system $S(\theta ,\phi ,r)$ .

PHI

( REAL) Angle $\phi$ in the old system $S(\theta ,\phi ,r)$ .

THPRIM

( REAL) Angle $\theta \text{'}$ in the new system $S\text{'}(\theta \text{'},\phi \text{'},r)$ .

PHPRIM

( REAL) Angle $\phi \text{'}$ in the new system $S\text{'}(\theta \text{'},\phi \text{'},r)$ .

THAX,PHAX

( REAL) Angles defining the axis of rotation in the old system $S(\theta ,\phi ,r)$ .

ROTANG

( REAL) Angle in the old system through which the system is rotated.

Method:

THETA and PHI are converted to a unit vector in Cartesian coordinates; THAX, PHAX and ROTANG are converted to a tensor, which is used to obtain a vector in the new system of axes giving THPRIM and PHPRIM.

Notes:

If THPRIM is very small, PHPRIM is badly defined.
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F110