rotations.md

description
Rotating frames.

Rotations

A vector whose x,y,z components are $$x,y,z$$ respectively is represented as the column matrix$$\begin{bmatrix}x\y\z\end{bmatrix}$$

Rotation of vectors in 2D:

In two dimensions, the standard rotation matrix has the following form:-

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The above matrix represents the counterclockwise rotation of a vector through angle θ. The vector in this figure is initially aligned with the x-axis

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If a vector $$\begin{bmatrix}x\y\end{bmatrix}$$ is rotated counterclockwise by $$\theta$$, the resultant vector $$\begin{bmatrix}x'\y'\end{bmatrix}$$ is given as

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Rotation of vectors in 3D:

The following matrices represent counterclockwise rotations by angle $$\theta$$ about the x,y and z axes respectively.

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Their usage is similiar as that explained in the previous section.

For the applications of rotations in UAVs, refer to the following link:

{% file src="../.gitbook/assets/AE321_EqMotion.pdf" %} Flight Mechanics {% endfile %}