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\title{Summary of my work on Satellite Constellations}
\author{William King}

\begin{document}
\maketitle

\section{Introduction}
\subfile{sections/00_Introduction} %Currently from past semesters.
%roughly done 2021-07-15

%Describe sections
The paper is organized as follows.
\cref{SEC:Environment}, describes the laws of motion 
governing satellites and debris(\ref{SEC:Laws})%, 
%places limits on various measures of risk (\ref{SEC:Survival}),
and reviews various definitions of kessler syndrome in 
the context of dynamic modeling, their advantages, and their disadvanteges (\ref{SEC:Kessler}).
In \cref{SEC:Models} the dynamic problem faced by constellation operators and 
social planners is first described.
Finally \cref{SEC:Computation} describes the computational approach and results.


\section{Modeling the Environment}\label{SEC:Environment}
\subsection{Laws of motion}\label{SEC:Laws}
\subfile{sections/01_LawsOfMotion} %Roughly done 2021-07-15

%\subsection{Marginal survival rates}\label{SEC:Survival}
%\subfile{sections/03_SurvivalAnalysis} %roughly done 2021-07-14
% Thoughts on removal: This doesn't add much to the actual questions.
% It is interesting, but as a paper is just too much.
% I'll keep it here to add it back easily.

\subsection{Kessler Syndrome}\label{SEC:Kessler}
\subfile{sections/02_KesslerSyndrome}  %roughly done before 2021-07-14
\subfile{sections/06_KesslerRegion}  %roughly done before 2021-07-14




\section{Model}\label{SEC:Models}
\subsection{Constellation Operator's Program}\label{SEC:Operator}
\subfile{sections/04_ConstellationOperator} %TODO

\subsection{Social Planner's Program}\label{SEC:Planner}
\subfile{sections/05_SocialPlanner} %TODO

\section{Computation}\label{SEC:Computation}
\subfile{sections/07_ComputationalApproach} %TODO

\section{Conclusion}\label{SEC:Conclusion}

\newpage
\section{References}
\printbibliography
\newpage
\section{Appedicies}
\subsection{Mathematical Notation}
Needs completed.
%\subsection{Deriving Marginal Survival Rates}\label{APX:Derivations:SurvivalRates}
%\subfile{sections/apx_01_MarginalSurvivalRates} 

\subsection{Deriving Euler Equations}\label{APX:Derivations:EulerEquations}
\subfile{sections/apx_02_GeneralizedEuEqSteps} 


\subsection{Collected Assumptions and Caveats}\label{APX:CollectedAssumptions}
I hope to write a section clearly explaining assumptions, caveats, and shortcomings here.
These will later get written back into the other sections, but I want to collect them 
in a single place first.
%time periods are long enough for debris to disperse after collisions.
%Only a single type of debris
%With my current computational idea; each constellation provides the same risk to each other constellation
% That can be easily adjusted in the computational models.

\end{document}

%%% Notes to keep track of
% Possible other things to investigate
%   - Free-entry conditions: which of the following?
%       - When for every operator, the current stocks imply no more launches(x = 0).
%       - When for every type of operator, the current stocks plus an own stock of 0 imply no more launches(x = 0).
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