Kinematrics
Mathematics for relating coordinate systems (frames), and calculating positions, angles and motions.
All bodies are rigid and forces aren’t considered.
Notes
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$$ \newcommand{\R}{\mathbb{R}}
\newcommand{\N}{\mathbb{N}}
\newcommand{\Z}{\mathbb{Z}}
\newcommand{\C}{\mathbb{C}}
\newcommand{\dx}{\text{ dx}}
\newcommand{\rang}{\text{rang}}
\newcommand{\s}{\ \ \ \ \ \ }
\newcommand{\arrows}{\s \Leftrightarrow \s}
\newcommand{\Arrows}{\s \Longleftrightarrow \s}
\newcommand{\arrow}{\s \Rightarrow \s}
\newcommand{\c}{\bcancel}
\newcommand{\v}[2]{
\begin{pmatrix}
#1 \\
#2 \\
\end{pmatrix}
}
\newcommand{\vt}[3]{
\begin{pmatrix}
#1 \\
#2 \\
#3 \\
\end{pmatrix}
}
\newcommand{\stack}[2]{
\substack{
#1 \\
#2
}
}
\newcommand{\atom}[3]{
\substack{
#1 \\
#2
}
\ce{#3}
}
$$