3DAttitude/CustomMath.sty at master · e271828e/3DAttitude · GitHub

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\ProvidesPackage{CustomMath}
\RequirePackage{amsmath}
\RequirePackage{amssymb}
\RequirePackage{latexsym}
\RequirePackage{verbatim}

%useful packages:
%dcolumn
%enumerate
%paralist
%multicol
%xspace

\DeclareMathOperator{\sgn}{sgn}
\DeclareMathOperator{\traceop}{tr}
\DeclareMathOperator{\atan2}{atan2}

%general purpose
\newcommand{\dq}[1]{``#1''}
\newcommand{\eql}[2]{\begin{equation} \label{#1} {#2} \end{equation}}
\newcommand{\eqnl}[1]{\begin{equation*} {#1} \end{equation*}}
\newcommand{\matenv}[1]{\begin{pmatrix} #1 \end{pmatrix}} %for whatever reason, the content of a matrix environment cannot be enclosed in braces

%basic objects
\newcommand{\basisopt}[1][ ]{\mathcal{E}_{#1}} %basis
\newcommand{\basis}[1][ ]{\mathcal{E}_{#1}} %basis
\newcommand{\vabs}[1]{\vec{\symbf{#1}}} %abstract vector
\newcommand{\mat}[1]{\symbf{#1}} %generic matrix
\newcommand{\mcol}[1]{\symbf{#1}} %matrix column (usually representation of a vector)
\newcommand{\comp}[1]{\symit{#1}} %matrix component (column or otherwise)

%aliases
\newcommand{\bv}{e} %basis vector
\newcommand{\orthm}{R} %generic orthogonal matrix symbol
\newcommand{\aut}{\Gamma} %generic automorphism symbol
\newcommand{\rotm}{\orthm} %generic rotation matrix symbol
\newcommand{\rotax}{n} %rotation axis
\newcommand{\rotang}{\vartheta} %rotation angle
\newcommand{\rotvecsymb}{\rho} %rotation vector symbol
\newcommand{\Eulersymb}{\Psi} %rotation vector symbol
\newcommand{\angvelsymb}{\omega} %angular velocity symbol
\newcommand{\angaccsymb}{\alpha} %angular acceleration symbol
\newcommand{\unitq}{r} %generic unit quaternion symbol
\newcommand{\rotq}{\unitq} %generic rotation quaternion symbol

%notation for indexing, resolving and subscripting vector and matrix quantities and combinations thereof
\newcommand{\ind}[2]{#1_{(#2)}}
\newcommand{\prj}[2]{#1^{#2}} %1: magnitude, 2: resolving frame
\newcommand{\sub}[2]{#1_{#2}} %defines a subscripted magnitude (1:magnitude, 2: subscript)
\newcommand{\rel}[3]{#1_{#2 #3}} %defines a relative magnitude (1: magnitude, 2: reference, 3: target)
\newcommand{\subprj}[3]{\prj{\sub{#1}{#2}}{#3}} %defines the scalar representation of a subscripted magnitude projected on a certain resolving frame (1: magnitude, 2: subscript, 3: resolving frame)
\newcommand{\relprj}[4]{\prj{\rel{#1}{#2}{#3}}{#4}} %defines the scalar representation of a relative magnitude projected on a certain resolving frame (1: magnitude, 2: reference, 3: target, 4: resolving frame)

%indexed, resolved, subscripted and relative vectors
\newcommand{\vasub}[2]{\sub{\vabs{#1}}{#2}} %subscripted abstract vector
\newcommand{\varel}[3]{\rel{\vabs{#1}}{#2}{#3}} %relative abstract vector
\newcommand{\vprj}[2]{\prj{\mcol{#1}}{#2}} %column matrix representation of a vector magnitude with explicit resolving basis
\newcommand{\vsub}[2]{\sub{\mcol{#1}}{#2}} %column matrix representation of a subscripted vector magnitude
\newcommand{\vrel}[3]{\rel{\mcol{#1}}{#2}{#3}} %column matrix representation of a relative vector magnitude
\newcommand{\vsubprj}[3]{\subprj{\mcol{#1}}{#2}{#3}} %column matrix representation of a subscripted relative vector magnitude
\newcommand{\vrelprj}[4]{\relprj{\mcol{#1}}{#2}{#3}{#4}} %column matrix representation of a relative vector magnitude with explicit resolving basis
\newcommand{\vprjdot}[2]{\prj{\dot{\mcol{#1}}}{#2}} %time derivative of a column matrix representation of a vector magnitude with explicit resolving basis
\newcommand{\vrelprjdot}[4]{\relprj{\dot{\mcol{#1}}}{#2}{#3}{#4}} %time derivative of column matrix representation of a relative vector magnitude with explicit resolving basis

%matrix representations
\newcommand{\AutM}[2]{\mat{\aut}^{#1}_{#2}} %matrix representation of an automorphism (1:reference, 2: target)
\newcommand{\RotM}[2]{\mat{\rotm}^{#1}_{#2}} %matrix representation of a rotation (1:reference, 2: target)
\newcommand{\RotMDot}[2]{\dot{\mat{\rotm}}^{#1}_{#2}} %matrix representation of a rotation (1:reference, 2: target)

%component representations
\newcommand{\cmp}[2]{\comp{#1}_{(#2)}} %vector component
\newcommand{\cmpsub}[3]{\comp{#1}_{{#2}({#3})}} %component of a subscripted vector magnitude
\newcommand{\cprj}[3]{\comp{#1}^{#2}_{({#3})}} %component of a vector magnitude with explicit resolving basis
\newcommand{\crel}[4]{\comp{#1}_{{#2}{#3}(#4)}} %component of a relative vector magnitude
\newcommand{\csubprj}[4]{{\comp{#1}^{#3}_{{#2}(#4)}}} %component of a subscripted vector magnitude with explicit resolving basis
\newcommand{\crelprj}[5]{\comp{#1}^{#4}_{{#2}{#3}(#5)}} %component of a relative vector magnitude with explicit resolving basis
\newcommand{\cAut}[3]{\csubprj{\aut}{#2}{#1}{#3}} %component representation of an automorphism (1: original, 2: target)
\newcommand{\cRotM}[3]{\csubprj{\rotm}{#2}{#1}{#3}} %component representation of a rotation (1: original, 2: target)

%basic operators
\newcommand{\rndp}[1]{\left({#1}\right)}
\newcommand{\vskew}[1]{\left[{#1}^{\times}\right]}
\newcommand{\norm}[1]{\left|{#1}\right|}
\newcommand{\abs}[1]{\left|{#1}\right|}
\newcommand{\tr}[1]{{#1}^{T}}
\newcommand{\trp}[1]{\tr{\rndp{{#1}}}}
\newcommand{\inv}[1]{{#1}^{-1}}
\newcommand{\invp}[1]{\inv{\rndp{{#1}}}}
\newcommand{\trace}[1]{\traceop {#1}}
\newcommand{\sign}[1]{\sgn \left({#1}\right)}

%specific vectors
\newcommand{\nullv}{\mcol{0}}
\newcommand{\rotv}[3][ ]{\vrelprj{\rotvecsymb}{#2}{#3}{#1}}
\newcommand{\normrotv}[2]{\norm{\vrel{\rotvecsymb}{#1}{#2}}}
\newcommand{\angacc}[3]{\vrelprj{\angaccsymb}{#1}{#2}{#3}}
\newcommand{\angvel}[3]{\vrelprj{\angvelsymb}{#1}{#2}{#3}}
\newcommand{\angveldot}[3]{\vrelprjdot{\angvelsymb}{#1}{#2}{#3}}
\newcommand{\rotvdot}[3]{{\dot{\mcol{\rotvecsymb}}}_{{#1}{#2}}^{#3}}
\newcommand{\cangvel}[4]{{\angvelsymb}^{#3}_{{#1}{#2}(#4)}}
\newcommand{\cangacc}[4]{{\angaccsymb}^{#3}_{{#1}{#2}(#4)}}

%specific matrices
\newcommand{\NullM}{\mat{0}}
\newcommand{\IdM}{\mat{I}}
\newcommand{\RotMAxAng}[2]{\mat{\rotm}_{\rotax\rotang}\rndp{{{#1}}, {{#2}}}}
\newcommand{\RotMRotV}[1]{\mat{\rotm}_{\rotvecsymb}\rndp{{#1}}}
\newcommand{\RotMQuat}[1]{\mat{\rotm}_{\quat{\rotq}}\rndp{{#1}}}
\newcommand{\RotMEuler}[3]{\mat{\rotm}_{\Eulersymb}\rndp{{{#1}}, {{#2}}, {{#3}}}}
\newcommand{\AngVelSkew}[3]{\vrelprj{\Omega}{#1}{#2}{#3}}
\newcommand{\RotEuler}[2]{\vrel{\Eulersymb}{#1}{#2}}

%quaternions
\newcommand{\quat}[1]{\symbfup{#1}} %quaternion font
\newcommand{\qcmp}[2]{{#1}_{(#2)}}
\newcommand{\qreal}[1]{\qcmp{#1}{0}}
\newcommand{\qvec}[1]{\mcol{#1}}
\newcommand{\qcol}[3][0ex]{\left[ \begin{matrix} {#2}\\[#1] {#3} \end{matrix} \right]} %the content of a matrix environment must not be enclosed in braces
\newcommand{\qcolcmp}[5][0ex]{\left[ \begin{matrix} {#2}\\[#1] {#3}\\[#1] {#4}\\[#1] {#5} \end{matrix} \right]} %4-component column notation with optional vertical spacing
\newcommand{\qi}{\symbfup{i}}
\newcommand{\qj}{\symbfup{j}}
\newcommand{\qk}{\symbfup{k}}
\newcommand{\qcon}[1]{{#1}^{*}}
\newcommand{\qconp}[1]{\left({#1}\right)^{*}}
\newcommand{\qprod}{\odot}
\newcommand{\qnorm}[1]{\left\|{#1}\right\|}
\newcommand{\RotQAxAng}[2]{\quat{\rotq}_{\rotax \rotang}\rndp{{{#1}}, {{#2}}}}
\newcommand{\RotQ}[2]{\quat{\rotq}^{#1}_{#2}} %attitude quaternion (1:reference, 2: target)
\newcommand{\RotQdot}[2]{\dot{\quat{\rotq}}^{#1}_{#2}}
\newcommand{\RotQcon}[2]{\qcon{\left( \RotQ{#1}{#2} \right)}}
\newcommand{\RotQdotcon}[2]{\qcon{\left( \RotQdot{#1}{#2} \right)}}
\newcommand{\RotQEuler}[3]{\quat{\rotq}_{\Eulersymb}\rndp{{{#1}}, {{#2}}, {{#3}}}}
\newcommand{\RotQRotV}[1]{\quat{\rotq}_{\rotvecsymb}\rndp{{#1}}}
\newcommand{\qprj}[2]{\quat{#1}^{#2}}
\newcommand{\cRotQ}[3]{\csubprj{\rotq}{#2}{#1}{#3}} %component representation of a rotation (1: original, 2: target)
\newcommand{\reRotQ}[2]{\cRotQ{{#1}}{{#2}}{0}}
\newcommand{\imRotQ}[2]{\mcol{\rotq}^{#1}_{#2}}
\newcommand{\qvangv}[1]{\qvec{\angvelsymb} \mkern-2mu \left({#1}\right)}


\begin{comment}
Command tests:
\prj{v}{a}
\sub{v}{a}
\rel{v}{\alpha}{\beta}
\subprj{v}{a_1}{\gamma}
\relprj{u}{\alpha}{\beta}{\gamma}
\vpsub{v}{a}
\varel{v}{\alpha}{\beta}
\vsub{v}{a}
\vrel{v}{\alpha}{\beta}
\vsubprj{v}{a}{\gamma}
\vrelprj{u}{\alpha}{\beta}{\gamma}
\ind{{\relprj{u}{\alpha}{\beta}{\gamma}}}{j}
\basisopt
\basisopt[\alpha]
\AutC{\alpha}{\beta}{3,2}
\cRotM{\alpha}{\beta}{i,j}
\AutM{\alpha}{\beta}
\RotM{\alpha}{\beta}

\cmp{x}{1}
\csub{x}{a}{1}
\cprj{x}{\gamma}{j}
\crel{x}{\alpha}{\beta}{k}
\csubprj{x}{\alpha}{\gamma}{3}
\crelprj{x}{\alpha}{\beta}{\gamma}{3}

\end{comment}

\endinput