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dissertation_macros.tex
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% CUSTOM MACROS
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newcommand{\linearize}[3]{\ensuremath{\left. \frac{\partial #1}{\partial #2} \right|_{#3} \delta #2}}
\newcommand{\norm}[1]{\ensuremath{\left\| #1 \right\|}}
\newcommand{\abs}[1]{\ensuremath{\left| #1 \right|}}
\newcommand{\Real}[1]{\ensuremath{\Re \left\{ #1 \right\}}}
\newcommand{\bracket}[1]{\ensuremath{\left[ #1 \right]}}
\newcommand{\braces}[1]{\ensuremath{\left\{ #1 \right\}}}
\newcommand{\parenth}[1]{\ensuremath{\left( #1 \right)}}
\newcommand{\pair}[1]{\ensuremath{\langle #1 \rangle}}
\newcommand{\met}[1]{\ensuremath{\langle\langle #1 \rangle\rangle}}
\newcommand{\refeqn}[1]{(\ref{eqn:#1})}
\newcommand{\reffig}[1]{Fig.~\ref{fig:#1}}
\newcommand{\tr}[1]{\mathrm{tr}\ensuremath{\negthickspace\bracket{#1}}}
\newcommand{\trs}[1]{\mathrm{tr}\ensuremath{[#1]}}
\newcommand{\deriv}[2]{\ensuremath{\frac{\partial #1}{\partial #2}}}
\newcommand{\dderiv}[2]{\ensuremath{\frac{\partial^2 #1}{\partial^2 #2}}}
\newcommand{\dderivc}[3]{\ensuremath{\frac{\partial #1}{\partial #2 \partial #3}}}
\newcommand{\diff}[2]{\ensuremath{\frac{d #1}{d #2}}}
\newcommand{\ddiff}[2]{\ensuremath{\frac{d^2 #1}{d #2^2}}}
\newcommand{\dirDiff}[2]{\ensuremath{\mathbf{D}_{#2} #1 \cdot \delta #2}} % directional derivative
\newcommand{\SO}{\ensuremath{\mathsf{SO(3)}}}
\newcommand{\T}{\ensuremath{\mathsf{T}}}
\renewcommand{\L}{\ensuremath{\mathsf{L}}}
\renewcommand{\so}{\ensuremath{\mathfrak{so}(3)}}
\newcommand{\SE}{\ensuremath{\mathsf{SE(3)}}}
\newcommand{\se}{\ensuremath{\mathfrak{se}(3)}}
\newcommand{\R}{\ensuremath{\mathbb{R}}}
\newcommand{\aSE}[2]{\ensuremath{\begin{bmatrix}#1\\0&1\end{bmatrix}}}
\newcommand{\ase}[2]{\ensuremath{\begin{bmatrix}#1\\0&0\end{bmatrix}}}
\newcommand{\D}{\ensuremath{\mathbf{D}}}
\newcommand{\Sph}{\ensuremath{\mathsf{S}}}
\renewcommand{\S}{\Sph}
\newcommand{\J}{\ensuremath{\mathbf{J}}}
\newcommand{\Ad}{\ensuremath{\mathrm{Ad}}}
\newcommand{\intp}{\ensuremath{\mathbf{i}}}
\newcommand{\extd}{\ensuremath{\mathbf{d}}}
\newcommand{\hor}{\ensuremath{\mathrm{hor}}}
\newcommand{\ver}{\ensuremath{\mathrm{ver}}}
\newcommand{\dyn}{\ensuremath{\mathrm{dyn}}}
\newcommand{\geo}{\ensuremath{\mathrm{geo}}}
\newcommand{\Q}{\ensuremath{\mathsf{Q}}}
\newcommand{\G}{\ensuremath{\mathsf{G}}}
\newcommand{\g}{\ensuremath{\mathfrak{g}}}
\newcommand{\Hess}[1]{\ensuremath{\mathrm{Hess} \, #1}}
\newcommand{\refprop}[1]{Proposition~\ref{prop:#1}}
% TODO Add a \vec macro that I use for all vectors in the paper
\newcommand{\vc}[1]{\ensuremath{#1}}
\newcommand{\vh}[1]{\hat{\vc{#1}}}
\newcommand{\vecbf}[1]{\bm{#1}}
\newcommand{\vb}[1]{\bm{#1}}
\newcommand{\slfrac}[2]{\left.#1\middle/#2\right.}
% SI UNITS
\newcommand{\usd}[2]{\SI{#1}[\$\ensuremath{\,}]{#2}}
\DeclareSIUnit\year{yr}
\DeclareSIUnit\siderealhour{sidereal~hr}
\DeclareSIUnit\solarsec{solar~sec}
\DeclareSIUnit\julianday{JD}
\DeclareSIUnit\px{px}
% proposition enviornments and proofs
\newcommand{\squeezeup}{\vspace{-2.5mm}}
\theoremstyle{definition}
\newtheorem{definition}{Definition}
\newtheorem{lem}{Lemma}
\newtheorem{prop}{Proposition}
\newtheorem{cor}{Corollary}
\newtheorem{remark}{Remark}
% Custom citation command for full cite in presentations - just show author, title, and y ear
\newcommand{\citecompact}[1]{\citeauthor{#1}, \citetitle{#1}, \citeyear{#1}}
% 2015 AAS Paper
% custom macros for AAS paper
% Poincar\'e correct name
\newcommand{\Poincare}{Poincar\'e }
% Macros for discrete states to save some time typing
\newcommand{\xk}{\ensuremath{x_k}}
\newcommand{\xkp}{\ensuremath{x_{k+1}}}
\newcommand{\yk}{\ensuremath{y_{k}}}
\newcommand{\ykp}{\ensuremath{y_{k+1}}}
\newcommand{\pxk}{\ensuremath{p_{x_k}}}
\newcommand{\pxkp}{\ensuremath{p_{x_{k+1}}}}
\newcommand{\pyk}{\ensuremath{p_{y_k}}}
\newcommand{\pykp}{\ensuremath{p_{y_{k+1}}}}
\newcommand{\xdotk}{\ensuremath{\dot{x}_{k}}}
\newcommand{\ydotk}{\ensuremath{\dot{x}_{k}}}
\newcommand{\xdotkp}{\ensuremath{\dot{x}_{k+1}}}
\newcommand{\ydotkp}{\ensuremath{\dot{y}_{k+1}}}
\newcommand{\distonek}{\ensuremath{r_{1_k}}}
\newcommand{\distonekp}{\ensuremath{r_{1_{k+1}}}}
\newcommand{\disttwok}{\ensuremath{r_{2_{k}}}}
\newcommand{\disttwokp}{\ensuremath{r_{2_{k+1}}}}
% costate equations of motion (gauss jordan elimination)
\newcommand{\fonex}{\ensuremath{f_{1_x}}}
\newcommand{\ftwox}{\ensuremath{f_{2_x}}}
\newcommand{\fthreex}{\ensuremath{f_{3_x}}}
\newcommand{\ffourx}{\ensuremath{f_{4_x}}}
\newcommand{\foney}{\ensuremath{f_{1_y}}}
\newcommand{\ftwoy}{\ensuremath{f_{2_y}}}
\newcommand{\fthreey}{\ensuremath{f_{3_y}}}
\newcommand{\ffoury}{\ensuremath{f_{4_y}}}
\newcommand{\fonexd}{\ensuremath{f_{1_{\dot x}}}}
\newcommand{\ftwoxd}{\ensuremath{f_{2_{\dot x}}}}
\newcommand{\fthreexd}{\ensuremath{f_{3_{\dot x}}}}
\newcommand{\ffourxd}{\ensuremath{f_{4_{\dot x}}}}
\newcommand{\foneyd}{\ensuremath{f_{1_{\dot y}}}}
\newcommand{\ftwoyd}{\ensuremath{f_{2_{\dot y}}}}
\newcommand{\fthreeyd}{\ensuremath{f_{3_{\dot y}}}}
\newcommand{\ffouryd}{\ensuremath{f_{4_{\dot y}}}}
% reference frame macros
\newcommand{\evec}[1]{\ensuremath{\vc{e}_{#1}}} % inertial reference frame
\newcommand{\fvec}[1]{\ensuremath{\vc{f}_{#1}}}
\newcommand{\bvec}[1]{\ensuremath{\vc{b}_{#1}}}
% Macros for derivartion of full body equations of motion
\newcommand{\ipos}{\ensuremath{x}}
\newcommand{\ivel}{\ensuremath{v}}
\newcommand{\iatt}{\ensuremath{R}}
\newcommand{\iangvel}{\ensuremath{\Omega}}
\newcommand{\iattvar}{\ensuremath{\eta}}
\newcommand{\ilinmom}{\ensuremath{p}}
\newcommand{\iangmom}{\ensuremath{\Pi}}
\newcommand{\apos}{\ensuremath{z}}
\newcommand{\aatt}{\ensuremath{R_A}}
\newcommand{\ahangvel}{\ensuremath{\hat{\Omega}_A}}
\newcommand{\spos}{\ensuremath{\rho}}
% relative macros
\newcommand{\rpos}{\ensuremath{x_r}}
\newcommand{\rvel}{\ensuremath{v_r}}
\newcommand{\ratt}{\ensuremath{R_r}}
\newcommand{\rdatt}{\ensuremath{\dot{R}_r}}
\newcommand{\rangvel}{\ensuremath{\Omega_r}}
\newcommand{\rhangvel}{\ensuremath{\hat{\Omega}_r}}
\newcommand{\rattvar}{\ensuremath{\eta_r}}
\newcommand{\rlinmom}{\ensuremath{p_r}}
\newcommand{\rangmom}{\ensuremath{\Pi_r}}
\newcommand{\rdangmom}{\ensuremath{\dot{\Pi}_r}}
% moment of inertia
\newcommand{\Jdr}{\ensuremath{J_{d_r}}}
\newcommand{\Jr}{\ensuremath{J_r}}
\newcommand{\Ji}{\ensuremath{J}}
\newcommand{\Jdi}{\ensuremath{J_d}}
\newcommand{\mass}[1]{\ensuremath{m_{#1}}}
\newcommand{\radius}[1]{\ensuremath{r_{#1}}}
\newcommand{\length}[1]{\ensuremath{l_{#1}}}
\newcommand{\brho}[1]{\ensuremath{\vc{\rho}_{#1}}}
% edit cref citations for IEEE format
\crefformat{equation}{(#2#1#3)} % no abbreviation for equation numbers
\Crefformat{equation}{Equation~(#2#1#3)} % no abbreviation for equation numbers
\crefrangeformat{equation}{(#3#1#4--#5#2#6)}
\Crefrangeformat{equation}{(#3#1#4--#5#2#6)}
\crefmultiformat{equation}{(#2#1#3)}{ and~(#2#1#3)}{, (#2#1#3)}{ and~(#2#1#3)}
% edit cref citations for IEEE format
\crefformat{figure}{Fig.~#2#1#3} % no abbreviation for equation numbers
\Crefformat{figure}{Fig.~#2#1#3} % no abbreviation for equation numbers
\crefrangeformat{figure}{Figs.~#3#1#4--#5#2#6}
\Crefrangeformat{figure}{Figs.~#3#1#4--#5#2#6}
\crefmultiformat{figure}{Figs.~#2#1#3}{ and~#2#1#3}{, #2#1#3}{ and~#2#1#3}
% for items in a list
\crefformat{enumi}{#2#1#3}
\Crefformat{enumi}{Item~#2#1#3}
\crefrangeformat{enumi}{(#3#1#4--#5#2#6)}
\Crefrangeformat{enumi}{Items~#3#1#4--#5#2#6}
\crefmultiformat{enumi}{#2#1#3}{ and~#2#1#3}{, #2#1#3}{ and~#2#1#3}
% for propositons
\crefformat{prop}{Proposition~#2#1#3} % no abbreviation for equation numbers
\Crefformat{prop}{Proposition~#2#1#3} % no abbreviation for equation numbers
\crefrangeformat{prop}{Propositions~#3#1#4--#5#2#6}
\Crefrangeformat{prop}{Propositions~#3#1#4--#5#2#6}
\crefmultiformat{prop}{Propositions~#2#1#3}{ and~#2#1#3}{, #2#1#3}{ and~#2#1#3}