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QTANG

QTANG

## Author

Craig B. Markwardt, NASA/GSFC Code 662, Greenbelt, MD 20770
craigm@lheamail.gsfc.nasa.gov
UPDATED VERSIONs can be found on my WEB PAGE:
http://cow.physics.wisc.edu/~craigm/idl/idl.html

## Purpose

Find rotation angle(s) of unit quaternion

Geometry

PHI = QTANG(Q)

## Description

The function QTANG accepts a unit quaternion Q and returns the
rotation angle PHI of the quaternion.
Use QTAXIS and QTANG to extract the properties of an existing
quaternion. Use QTCOMPOSE to combine a rotation axis and angle
into a new quaternion.
Conventions for storing quaternions vary in the literature and from
library to library. This library uses the convention that the
first three components of each quaternion are the 3-vector axis of
rotation, and the 4th component is the rotation angle. Expressed
in formulae, a single quaternion is given by:
Q(0:2) = [VX, VY, VZ]*SIN(PHI/2)
Q(3) = COS(PHI/2)
where PHI is the rotation angle, and VAXIS = [VX, VY, VZ] is the
rotation eigen axis expressed as a unit vector. This library
accepts quaternions of both signs, but by preference returns
quaternions with a positive 4th component.

## Inputs

Q - array of one or more unit quaternions. For a single
quaternion, Q should be a 4-vector. For N quaternions, Q
should be a 4xN array.

## Returns

For a single quaternion, returns the scalar quaternion rotation
angle in radians. For N quaternions, returns an N-vector of
rotation angles.

NONE

## Example

IDL> print, qtang(qtcompose([0d,1,0], !dpi/4))
0.78539816
Prints the angle part of the quaternion composed of a rotation of
!dpi/4 radians around the axis [0,1,0]

## See Also

QTANG, QTAXIS, QTCOMPOSE, QTERP, QTEXP, QTFIND, QTINV, QTLOG,
QTMAT, QTMULT, QTPOW, QTVROT

## Modification History

Written, July 2001, CM
Documented, Dec 2001, CM
Usage message, error checking, 15 Mar 2002, CM
\$Id: qtang.pro,v 1.6 2008/12/14 20:00:31 craigm Exp \$

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