-
Notifications
You must be signed in to change notification settings - Fork 2
/
Copy pathdefense_macros.tex
168 lines (144 loc) · 6.37 KB
/
defense_macros.tex
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 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}}}
\providecommand{\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}}}