I have been using a 6dof LSM6DS0 IMU unit (with accelerometer and gyroscope) and am trying to calculate the angle of rotation around all three axes. I have tried many methods but am not getting the results as expected. Methods tried: (i) Complementary filter approach – I am able to get the angles using the […]

I am studying rotations and in particular interpolation between 2 matrices $R_1,R_2 \in SO(3)$ which is: find a smooth path between the 2 matrices. I found some slides about it but not yet a good book, I asked the author of the slides and he told me he does not know about a good book […]

Sorry if the title is a bit cryptic. It’s the best I could come up with. First of all, this question is related to another question I posted here, but that question wasn’t posed correctly and ended up generating responses that may be helpful for some people who stumble upon the question, but don’t address […]

When I first learned about 2d rotation matrices I read that you represented your point in your new coordinate system. That is you take the dot product of your vector in its current coordinate system and against the new i and j vector in the rotated coordinate system. $\begin{bmatrix}\cos\theta&-\sin\theta\\\sin\theta&\cos\theta\end{bmatrix}p=p^\prime$ The columns represent the new i […]

I have a 3D point that is rotated about the $x$-axis and after that about the $y$-axis. I know the result of this transformation. Is there an analytical way to compute the rotation angles? $$ v’=R_y(\beta)*R_x(\alpha)*v $$ Here, $v$ and $v’$ are known and I want to compute $\alpha$ and $\beta$. $R_x$ and $R_y$ are […]

Is it possible to find the unit vector with: Roll € [-90 (banked to right), 90 (banked to left)], Pitch € [-90 (all the way down), 90 (all the way up)] Yaw € [0, 360 (N)] I calculated it without the Roll and it is \begin{pmatrix} cos(Pitch) sin(Yaw)\\ cos(Yaw) cos(Pitch)\\ sin(Pitch) \end{pmatrix}. How should it […]

Given this hyperbola $x_1^2-x_2^2=1$, how do I transform it into $y_1y_2=1$? When I factor the first equation I get $(x_1+x_2)(x_1-x_2)=1$, so I thought $y_1=(x_1+x_2)$ and $y_2=(x_1-x_2)$. Therefore the matrix must be $ \begin{pmatrix} 1&1\\1&-1 \end{pmatrix} $. But in maple it is just drawn as a straight line. However, it should be a rotated hyperbola. Is […]

The rotation group is isomorphic to the orthogonal group $SO(3)$. So a rotation matrix can represent all the possible rotation transformations on the euclidean space $R3$ obtainable by the operation of composition. The axis/angle notation describes any rotation that can be obtained by rotating a solid object around an axis passing on the reference origin […]

I would like to decompose an $n$-dimensional orthogonal rotation matrix (restricting to simple rotation with a single plane of rotation) to the two basis vectors of the plane of rotation, and an angle of rotation. The common method is decomposing the rotation matrix to an axis and angle, but this doesn’t work in higher dimensions. […]

Background: Let $S^2$ denote the unit sphere in $\mathbb{R}^3$. By “stereographic projection”, I mean the mapping from $S^2$ (remove the north pole) to the complex plane which sends \begin{align*} \begin{bmatrix} x \\ y \\ t \end{bmatrix} \in S^2 \mapsto z = \frac{x+iy}{1-t} \in \mathbb{C}. \end{align*} The inverse mapping, from the complex plane to the sphere, […]

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