statics Math Typesetting

Section C.2 Math Typesetting

Pay attention to details

Points look like $P\text{,}$ like other scalars.
Vectors look like $\vec{V}\text{,}$ markup as <m>\vec{V}</m>.
Scalars and variables are italic, like $A\text{,}$ or $T\text{,}$ markup as <m>T<m>.
Latex subscripts: variables should be italic, labels upright. $F_x$ vs. $M_\text{cut}.$
Vector subscripts should not be bold. $\vec{F}_x$ not $\vec{F_x}\text{.}$ markup as code <m>\vec{F}_x<m>
Use macros \ihat, \jhat, \khat for unit vectors.
Avoid \cdot for implied multiplication, it could be confused for dot product.
Put a space before differential quantities in integrals like so: y = \int x\; dx.
No parentheses around simple arguments of trig functions. Use $\sin \alpha\text{,}$ not $\sin (\alpha)\text{.}$ Use parentheses for ambiguous arguments $\sin (2 \pi f t).$

Notation.

Vector Notation

Table C.2.1. Vector Notation

Latex	Result	Notes
default \vec{}	$\vec{F}\text{,}$ $\vec{F}_x\text{,}$ $\vec{i}\text{,}$ $\vec{j}\text{,}$ $\vec{\alpha}\text{,}$ $\vec{\lambda}$	Greek letters are not bold
\ihat, \jhat, \khat	$\ihat\text{,}$ $\jhat\text{,}$ $\khat$	Use these, not \vec{i} etc.
\vecarrow	$\vecarrow{A}$
\overrightarrow	$\overrightarrow{A}$
\hat	$\hat{i}\text{,}$ $\hat{j}\text{,}$ $\hat{k}$
\textbf	$\textbf{F}\text{,}$ $\textbf{$\alpha$}$	\textbf{$\alpha$} doesn't work.
\mathbf	$\mathbf{F}\text{,}$ $\mathbf{\alpha}\text{,}$ $\mathbf{i}$	upright, but greek letters aren't bold.
\boldsymbol	$\boldsymbol{F}\text{,}$ $\boldsymbol{\alpha}\text{,}$ $\boldsymbol{\lambda}$	bold greek letters, but italic
\i \j (dotless)	$\i,$$\j$	doesn't work in MathJax
\imath, \jmath	$\imath\text{,}$ $\jmath$	italic and dotless

Figure SS – This interactive allows you to input the vector components of $\vec{F}_A$ and $\vec{F}_B$ and then compute the magnitude of the projection of $\vec{F}_A$ onto $\vec{F}_B$$\left \| \proj_{\vec{F}_B}\vec{F}_A \right \|\text{,}$ the vector projection of $\vec{F}_A$ onto $\vec{F}_B$ ($\proj_{\vec{F}_B}\vec{F}_A$) and also the vector portion of $\vec{F}_A$ which is perpendicular to $\vec{F}_B\text{.}$ Source:

Unit vectors without dots? http://www.tapdancinggoats.com/latex-vector-notation.htm

What notation for vector components?

$\vec{F} = (F_x, F_y, F_z)$ vs. $\vec{F} = \langle F_x, F_y, F_z \rangle\text{,}$ $\vec{F}=(20;\ang{30})$

What notation for polar representation? I want to use angles < 90° from a reference.

Absolute values, scalar components, matrices, determinants

Single or double bars for absolute value?

\begin{gather*} \left | \proj_{\vec{F}_B}\vec{F}_A \right |\\ \left \| \proj_{\vec{F}_B}\vec{F}_A \right \| \end{gather*}

Notation for matrices and determinants? I believe determinants are in vmatrix, matrices in bmatrix or matrix

\begin{align*} \vec{M} \amp = \vec{r} \times \vec{F}\\ \amp = \det \begin{bmatrix} \ihat \amp \jhat \amp \khat \\ r_x \amp r_y \amp r_z \\ F_x \amp F_y \amp F_z \end{bmatrix} = \begin{vmatrix} \ihat \amp \jhat \amp \khat \\ r_x \amp r_y \amp r_z \\ F_x \amp F_y \amp F_z \end{vmatrix} \\ \amp = (r_y F_z- r_z F_y) \ihat - (r_x F_z - r_z F_x)\jhat - (r_x F_y - r_y F_x)\khat \end{align*}

What is the best notation for the projection operation?

$\proj^{\vec{F}_A}_{\vec{F}_B}\text{,}$ or $\proj_{\vec{F}_A/\vec{F}_B} \text{,}$ or

$\proj_{\vec{F}_A,\vec{F}_B} \text{,}$ or $\proj_{\vec{F}_A}(\vec{F}_B)\text{.}$

Useful Macros.

I've defined some latex macros in docinfo.ptx so

\vec{A} will produce $\vec{A}$

\ihat will produce $\ihat$

\jhat will produce $\jhat$

\khat will produce $\khat$

\vecarrow{F} will produce $\vecarrow{F}$

\let\vecarrow\vec%
\renewcommand{\vec}{\boldsymbol}%
\newcommand{\ihat}{\mathbf {\boldsymbol{i}}}%
\newcommand{\jhat}{\mathbf {\boldsymbol{j}}}%
\newcommand{\khat}{\mathbf {\boldsymbol{k}}}%
\DeclareMathOperator{\proj}{proj}

Rotated measured angle.

\begin{align*} \vec{F} \amp = \N{100} @ \ang{30}~\measuredangle\\ \vec{F} \amp = \N{100} @ \ang{30}~\rotatebox[origin=c]{90}{$\measuredangle$}\\ \vec{F} \amp = \N{100} @ \ang{30}~\rotatebox[origin=c]{180}{$\measuredangle$}\\ \vec{F} \amp = \N{100} @ \ang{30}~\rotatebox[origin=c]{270}{$\measuredangle$} \end{align*}

\begin{gather*} \require{physics} \require{enclose} \enclose{circle}[mathcolor="blue"]{x}\\ \enclose{circle}[mathcolor="blue"]{\color{black}{x}}\\ \enclose{circle,box}{x}\\ \enclose{circle}{\enclose{box}{x}} \end{gather*}

\begin{gather*} \abs{A}\\ \norm{A} \end{gather*}

\begin{gather*} \require{HTML} \style{display: inline-block; transform: rotate(-90deg)}{\measuredangle}\\ \require{HTML} \style{display: inline-block; transform: rotate(90deg)}{\measuredangle} \end{gather*}

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