Linked Questions

60
votes
13answers
22k views

What's a good place to learn Lie groups?

Ok so I read the following article the other day: http://www.aimath.org/E8/ and I wanted to learn more about lie groups. Using my exceptional deduction skills I thought "oh it must have something to ...
15
votes
1answer
8k views

Exponential Function of Quaternion - Derivation

The equation for the exponential function of a quaternion $q = a + b i + c j + dk$ is supposed to be $$e^{q} = e^a (\cos(\sqrt{b^2+c^2+d^2})+\frac{(b i + c j + dk)}{\sqrt{b^2+c^2+d^2}} \sin(\sqrt{b^2+...
9
votes
3answers
4k views

Quaternions vs Axis angle

Whats the use of representing rotation with quaternions compared to normal axis angle representation? I've been trying to learn quaternions and they make enough sense but as far as I can tell ...
2
votes
2answers
6k views

Quaternions multiplication order (to rotate & unrotate)

Say, I have parent object rotation quaternion Qp & child object rotation (local - relative to parent) quternion Qch. 1) ...
2
votes
2answers
2k views

how to combine angle rotations along different axes into one rotation along a single vector [duplicate]

So, lets say I have some rotation a about the x-axis(vector:$(1, 0 ,0)$) and some other rotation about y-axis(vector $(0, 1, 0)$) and a rotation about the z-axis(vector: $(0,0,1)$). How would I ...
1
vote
2answers
887 views

Why does multiplying a Quaternion and a Vector yield these results?

Today I coded the multiplication of quaternions and vectors in Java. This is less of a coding question and more of a math question though: ...
0
votes
1answer
527 views

understanding quaternions - spatial rotations

I would like to know if my understanding about quaternions is correct please: lets say you have a vector in 3d space. You could rotate the x,y and-z frame on a fixed point so that it is parallel with ...
1
vote
1answer
204 views

Given a start point in 3d and a quaternion and length to Point B can you find Point B

Let's assume I have a start point A (x, y, z). Now the object has moved and the new orientation is given by a quaternion Q and it's pointing at point B which is L length away from it. How can I ...
0
votes
1answer
145 views

Calculating principal component of a quaternion

1In this paper (equation 5), the author is presenting an equation of quaternion multiplication of three arrays. The second array is 3x1 while the other two are 4x1. Also, the author uses 'principle ...
2
votes
0answers
111 views

Factoring quaternion into three parts

I am faced with a problem where I have a quaternion which represents rotation and three arbitrary axis about which I can make rotations, thus three unit vectors. What I would like to know is angles (...
2
votes
1answer
81 views

Angles of rotation

I am haunted by a problem of angles of rotation. Here's my nightmare. At the origin of an inertial frame $R_0(XYZ)$, there is a ball. Another reference frame $R(xyz)$ is fixed to the center of this ...