Questions regarding quaternions
- From: "Zerex71" <Zerex71@xxxxxxx>
- Date: 28 Feb 2007 11:33:48 -0800
Greetings,
I am implementing software that is going to make heavy use of
quaternions. I have found a plethora of information online but I
still have some questions that I would like to get some answers to:
1. In all of my reading, I understand that any method of mathematical
rotation (matrix multiplication, quaternions, etc.) can perform two
different tasks:
a. Take an object (e.g. vector) and rotate it in space to a new
desired orientation
b. Take a frame of reference (or measurements therein) and convert it
to another frame of reference (or measurements referenced that second
frame) without rotating it
I would like to get some clarification and explanation in my thinking
because it will really help me. When I think of situation a., I think
of an actual, physical rotation of a body (for example, if I pitch the
nose of a rocket up or down about its own inertial frame of reference,
sometimes called LVLH). When I think of situation b., I am not
physically rotating an object, but I want to take its angular
references in one coordinate frame of reference and calculate them
relative to another frame of reference (for example, if a vehicle is
pitched over so many degrees relative to some invisible inertial frame
of reference, but relative to another frame, has an entirely different
value for pitch). My question then is, Can both be done using
quaternions?
2. Let's say I have an orientation of a rocket on a launch pad,
perfectly vertical, tail facing due south, on a locally flat stretch
of land. Can I take a vector representing this situation and convert
it to a quaternion? Can I take the local launch pad xyz frame of
reference and convert it to a quaternion?
2. In looking at the p' = qpq^-1 quaternion transformation, that seems
to address situation a. above but not b. True or false?
3. When doing the p' = qpq^-1 quaternion transformation, you have a
vector and a quaternion. But where do I get the quaternion from? The
vector (or body under consideration) I obviously would have, but how
would I determine the quaternion?
4. When doing the p' = qpq^-1 quaternion transformation, is q (and
likewise, its inverse) a normalized quaternion? One of the
presentations I read seemed to indicate that q must be a unit
quaternion.
5. Does "normalization" basically mean taking a quaternion and
converting it to a "unit quaternion", just like when you take a vector
and divide by its magnitude to get a unit vector? Is a normalized
quaternion just a unit quaternion?
A lot of the reason I am interested in situation b. is that I will
want to work with a couple of different frames of reference for my
simulated shuttle vehicle: Earth-center, vehicle LVLH, and launch pad
are the three coordinate systems I would want to be able to switch
between. I imagine each as a little xyz set of axes like I often see
in math books, CAD programs, etc.
That should be enough for now. Thanks for taking the time to read.
Mike
.
- Follow-Ups:
- Re: Questions regarding quaternions
- From: cbrown
- Re: Questions regarding quaternions
- Prev by Date: Re: Nineteen months.
- Next by Date: Re: Circle Laying On Curves
- Previous by thread: Open Source Maths Package Wanted
- Next by thread: Re: Questions regarding quaternions
- Index(es):
Relevant Pages
|
|
