# Tagged Questions

153 views

### Understanding quaternions & gradient descent in a paper on inertial / magnetic sensor arrays

I hope this question is appropriate here! I and a friend at work are trying to understand Sebastian Madgwick's paper, "An efficient orientation for inertial and inertial/magnetic sensor arrays" ...
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### Small angular displacements with a quaternion representation

I have the orientation of a 3D spatial object represented by a unit quaternion: $$q = a_1 + a_2 i + a_3 j + a_4 k$$ $$\|q\| = (a_1^2 + a_2^2 + a_3^2 + a_4^2)^{1/2} = 1$$ I'd like to perturb this ...
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### Coordinate Transformation on Local coordinate system

I am having a point $P(x,y,z)$ in $3D$ with respect to global coordinate system. I want to create an another Local Coordinate System by picking three points $N1, N2, N3$ in 3D. Now I want to know the ...
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### Quaternions, torque, and impulse.

In a physics simulation I have a solid ball of mass $m$ and moment of interia $M$ (which is a diagonal matrix with all entries equal to ${2\over5}mr^2=i$). Its instantaneous rotation is given by a ...
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### Updating a quaternion orientation by a vector of euler angles

I'm trying to understand why this formula works to update an orientation with an angular velocity represented as a vector of rotations in $radians/{second}$. I understand that two quaternions ...
### How $v=(-\sin\frac{\alpha}{2}\sin\frac{\beta}{2},\cos\frac{\alpha}{2}\sin\frac{\beta}{2},\sin\frac{\alpha}{2}\cos\frac{\beta}{2})$ is derived from…
In the book Quarternion and Rotation Sequences, I can't seem to work out how the final equation (colored in $\color{red}{red}$) is derived from the original equation (colored in $\color{blue}{blue}$). ...