Quaternions for a continuous sequence of rotations?
- From: andy@xxxxxxxxxxxxxxxxxxxxxx (Andy Spragg)
- Date: Sat, 04 Jun 2005 00:32:34 GMT
Composition of quaternions allows us to calculate a single rotation
that is equivalent to a sequence of specified rotations, in which each
successive axis and angle of rotation need bear no relation to its
predecessor. Now think of a situation where the axis and angle change
continuously; the simplest I can think of is where a solid body
rotates at a constant angular velocity, about an axis which changes
smoothly as a specified function of time. Can quaternions still be
used here? I mean, obviously the problem could be numerically
approximated as a sequence of rotations dt apart, and I have no
(great) trouble believing that the result of the calculation would
tend to a well-defined limit as dt tended to zero. What is not at all
clear to me, however, is whether this limit would be the same as the
result of the continuous process, rotations being the slippery chaps
that they are. Can anyone help me out, please (references would be
great)? Hopefully,
Andy
.
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