11 questions linked to/from Representing rotations using quaternions
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### 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 ...
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### 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+...
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### 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 ...
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### Quaternions multiplication order (to rotate & unrotate)

Say, I have parent object rotation quaternion Qp & child object rotation (local - relative to parent) quternion Qch. 1) ...
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### 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 ...
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### 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: ...
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### 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 ...
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### 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 ...
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### 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 ...
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 ...