Tagged Questions

19 views

21 views

What are the coordinates of a point on a rigid body after a rotation in 3D Euclidean space, given the initial coordinates and a center of rotation

Main question Let ($x_p$, $y_p$, $z_p$) be the initial coordinates of a point $P$ on a rigid body in a right-handed 3D Euclidean space. Let ($x_r$, $y_r$, $z_r$) be the coordinates of a center of ...
30 views

Rotation of axes give the same point in space?

I am playing around with rotation of axes formulas and not getting it. I don't understand how this rotates anything when it is just giving you different coordinates for the SAME point in space. How ...
56 views

rotation matrix to axis angle

from wikipedia the above rotation matrix has a rotation of -74 degrees. What does it mean "around the axis (−1⁄3,2⁄3,2⁄3)"? How can I determine how many degrees is rotated on X axis, Y axis and Z ...
25 views

Rotation of velocity vectors in Cartesian Coordinates

I want to rotate a $(X,Y,Z)$ coordinate-system around it $Z$-axis. For the coordinates this can be done with the rotation matrix:  R_Z(\theta)= \begin{pmatrix} cos \theta & -\sin(\theta) & ...
28 views

How to move coordinate systems using rotation matrices.

I am having some trouble with this question. I understand that the rotation matrix will be 4x4 and that the first 3 columns will just be $u$, $v$ and $n$ transposed but I dont know what I am ...
75 views

Converting Euler Angle z-y'-x'' sequence to heading

I'm trying to convert a set of Euler Angles to a heading $(0-360)$ degrees. The Euler Angles use the $\ x-y'-x''$ sequence headings, using $\ \psi, \theta, \phi$ as the rotation angles, respectively. ...
17 views

Proving the existence of a ____ number of conditions under a rotation of coordinates.

I'm reading a section on Rotation of Coordinate Systems and this is throwing me off: 'In n-dimensional space, the rotation matrix will have $n^2$ elements, upon which orthogonality relations place ...
174 views

Reverse rotation back to original coordinates (Euler Angles)

so in the program I'm trying to write (still, it's a mathematical question) I have a set of coordinates and angles (Euler angles) which represent the place and orientation of an object in space, ...
184 views