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Added a coordinate frame transformation for checking the syntax.
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iamazadi committed Sep 9, 2024
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Expand Up @@ -4,4 +4,4 @@ Description = "How the reaction wheel unicycle works."

# The Reaction Wheel Unicycle

``{}_{w2}^{cp}T = \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & cos(\alpha) & sin(\alpha) & 0 \\ 0 & -sin(\alpha) & cos(\alpha) & 0 \\ 0 & 0 & 0 & 1 \end{bmatrix} \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & r_w & 1 \end{bmatrix} = \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & cos(\alpha) & sin(\alpha) & 0 \\ 0 & -sin(\alpha) & cos(\alpha) & 0 \\ 0 & -r_w sin(\alpha) & r_w cos(\alpha) & 1 \end{bmatrix}``
``{}_{w2}^{cp}T = \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & cos(\alpha) & -sin(\alpha) & 0 \\ 0 & sin(\alpha) & cos(\alpha) & 0 \\ 0 & 0 & 0 & 1 \end{bmatrix} \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & r_w \\ 0 & 0 & 0 & 1 \end{bmatrix} = \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & cos(\alpha) & -sin(\alpha) & -r_w sin(\alpha) \\ 0 & sin(\alpha) & cos(\alpha) & r_w cos(\alpha) \\ 0 & 0 & 0 & 1 \end{bmatrix}``

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