# Tagged Questions

This tag is for questions about *rotations*: a type of rigid motion in a space.

30 views

### Finding normal of arbitrarily oriented ellipsoid

For an axis-aligned ellipsoid, the equation is $$\frac{x^2}{a^2} + \frac{y^2}{b^2} + \frac{z^2}{c^2} = 1.$$ With $a=b$ this will give a spheroid with the $z$ axis as its symmetry axis. A spheroid ...
15 views

### Individual components of a quaternion?

My 3D system consists of a global coordinate frame and a quaternion in this frame represents a roll (about x), pitch (about y) and yaw (about z) in the form of four values (qx, qy, qz, qw). How can I ...
18 views

### Subtracting Direction cosine matrices

Say I have a rotation matrix $C(q) \in R^{3\times3}$ which is a function of a Hamilton quaternion $q=[q_w, q_x, q_y, q_z]^T=[q_w, q_v]^T$ where $q_v$ is the vector part of the quaternion. The ...
34 views

### How to rotate a line based dimensions of a piece of paper

I have a line where I know the start and end point on a piece of paper with the dimensions of 8 1/2 inches x 11 inches. the start point is 5.6 inches from the right of the paper and 4 inches down ...
58 views

### Decomposition to rotation around arbitrary axis

In 3d, I have a $4\times4$ matrix $M$, which has only a rotation part and a translation part. In other words, I can compute $X'=RX+T$ ( with $R$ a $3\times3$ rotation matrix, $T$ a vector for the ...
40 views

### Can Someone help me with my trigonometry rotation, formula? [closed]

I've been working on some code for a game to make a hit box, this question is just about the math though. Basically I'm trying to rotate an X, Y point(i guess according to the game it's Z,X Not sure ...
64 views

### Compute $R^{2016}$ of a given counterclockwise rotation.

Write out the matrix $R$ of counterclockwise rotation by 30$^{\circ}$ in $\mathbb{R}^2$. Compute ${R}^{2016}$. Now this is an easy question to answer overall; 30 goes into 360 12 times and one twelfth ...
36 views

### Quaternion Rotation

I am modelling rotations of a rectangular box (3 dimensions) in Matlab using Quaternion theory. Using the theory found on https://en.wikipedia.org/wiki/Quaternions_and_spatial_rotation I have ...
29 views

### matrix multiplied by rotation matrix on right side and transpose(rotation) on left side

Would a matrix remain un-rotated if it is multiplied by an orthonormal rotation matrix on right side and transpose of same rotation matrix on the left side?
25 views

### How to calculate the shortest rotation from current to the target angle? [closed]

In the following situation: My current angle is 40*, my target angle is 130*. How should I calculate the rotation that should be done to reach the target angle from the current one? I've done the ...
77 views

### The relation between axes of 3D rotations

Let's suppose we have two rotations about two different axes represented by vectors $v_1$ and $v_2$: $R_1(v_1, \theta_1)$, $R_2(v_2,\theta_2)$. It's relatively easy to prove that composition of ...
20 views

29 views

### Calculating a rotation matrix: error and properties

Given an axis $u=\begin{bmatrix} \sqrt 3/3, \sqrt 3 /3, \sqrt 3 /3 \end{bmatrix}$ and an angle $\phi =\frac{2\pi}{3}$ I want to calculate the related rotation matrix: Well given Rodriguez’s formula: ...
17 views

### Verifying that the Rodrigues formula gives the same result as $Rot(x,\phi)$?

How to verify that the Rodrigues formula with $x$ as an axis of rotation and $\phi$ the angle of rotation with $u$ a unit vector along $x$ and $Rot(x,\phi)$ gives the same result? I only know that ...
36 views

### Euler Angle + Distance to XYZ coordinate

Background I'm familiar with Euler Angles and 3d space systems but I'm having trouble with Rotation Matrices. Scenario I've converted my Euler Angle to degrees for ...
52 views

### Mathematical expression of a rotation

I don't understand how my teacher defined an expression for the rotation adding up the two red vectors made up from the strong blue ones after rotation I especially don't understand how does the ...
25 views

### Transformation of fourth rank tensor and its matrix form

I would like to calculate transformation of fourth rank tensor, $$C_{ijkl}=\Sigma_{m=1}^{3}\Sigma_{n=1}^{3}\Sigma_{p=1}^{3}\Sigma_{q=1}^{3}a_{im}a_{jn}a_{kp}a_{lq}C_{mnpq}$$ where $a_{xy}$ is ...
43 views

### Quaternion interpolation in 3D

I'm a chemist lost in the captivating world of mathematics thus if you could keep your answers simple it would be awesome! Here is my problem: I have two mobiles (A,B) in 3D. Ideally, I would like to ...
33 views

### What is the shape of an ellipse (or parabola) that has rotated around the x-axis?

What is the shape of an ellipse (or parabola) that has rotated around the x-axis? Is there a specific name?
42 views

### Alignment of one 3D Coordinate system to another 3D Coordinate system

I'm working on a project depicted by this picture(taken from internet) where there are different coordinate system involved which corresponds to camera coordinate system and local 3D coordinate system ...
Is there a nice, clean reference which lists a basis in terms of (linear combinations of) spherical harmonics for the $L^2$ space of functions defined on the sphere $\mathbb{S}^2$ which are invariant ...