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QTEXP

QTEXP

## 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

Compute "exponentiation" of a non-unit quaternion

Geometry

## Calling Sequence

Q = QTEXP(QLOG)

## Description

The function QTEXP computes the "exponentiation" of a quaternion.
The exponential is only defined for a non-unit quaternion with a
*zero* rotation angle. Specifically, the expression
QTEXP([VAXIS * PHI/2, 0])
becomes

[VAXIS*SIN(PHI/2), COS(PHI/2)]
where VAXIS is the unit vector rotation axis and PHI is the
rotation angle. Note that since VAXIS is a unit vector, the
product VAXIS*PHI can have an arbitrary direction and magnitude.
Typically the input to QTEXP is found by taking the logarithm of a
unit quaternion using QTLOG, and the identity QTEXP(QTLOG(Q)) is
the same as Q.

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

QLOG - a non-unit quaternion of the form [VX, VY, VZ, 0]; or,
N quaternions of the same form, as a 4xN array.

## Returns

The exponentiated unit quaternion(s). For a single input
quaternion, returns a 4-vector; for N input quaternions, returns a
4xN array.

NONE

## Example

IDL> print, qtlog(qtcompose([0d,1,0], !dpi/4))
0.0000000 0.39269908 0.0000000 0.0000000
Prints the logarithm of the quaternion composed of a rotation of
!dpi/4 radians around the axis [0,1,0]

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

## Modification History

Written, July 2001, CM
Documented, Dec 2001, CM
Documentation corrected, 27 Jan 2002, CM
Usage message, error checking, 15 Mar 2002, CM

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