Notation

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Acronyms and Initialisms

Symbol	Description
\(\{A\}\), \(\{G\}\), \(\{R\}\)	Reference frames
\(\{B\} \rightarrow \{{}^A_B R, {}^A P\}\)	Relative frame (frame \(\{B\}\) defined relative to \(\{A\}\))
\({}^A P = [P_x, P_y]^T\)	Point in a frame (upper case letters)
\({}^A v = [v_x, v_y]^T\)	Vector in a frame (lower case letters)
\({}^A_B R = \begin{bmatrix} \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{bmatrix}\)	Rotation matrix
\({}^A Q = {}^A_B R {}^A Q + {}^A P\)	Transformation/change in reference
\(q\)	Generalized coordinates (state or configuration)
\(\dot q\)	Generalized velocities (update equation)