```
\documentclass{article} %podeu treure el twocolumn si voleu una columna
\usepackage[utf8]{inputenc}
\usepackage{graphicx}
\usepackage{fancyhdr}
\usepackage{lastpage}
\usepackage{geometry}
\usepackage{lipsum}
\usepackage{relsize}
\usepackage{listings}
\usepackage{color}
\usepackage{amsmath}
\usepackage{amsthm}
\usepackage{enumerate}
\usepackage{array}
\usepackage{float}
\usepackage{hyperref}
\usepackage{cite}
\usepackage{multirow}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage[colorinlistoftodos]{todonotes}
\hypersetup{
colorlinks=true, % false: boxed links; true: colored links
linkcolor=black, % color of internal links
citecolor=black, % color of links to bibliography
filecolor=magenta, % color of file links
urlcolor=blue
}
\newgeometry{left=2.7cm, right=2.7cm, top=3.5cm, bottom=3.2cm}
\pagestyle{fancy}
\fancyfoot{}
\fancyhead{}
\fancyhf{}
\renewcommand{\headrule}{}
\renewcommand{\footrule}{}
\newcommand{\ui}{\overrightarrow{i}}
\newcommand{\uj}{\overrightarrow{j}}
\newcommand{\un}{\overrightarrow{n}}
\newcommand{\ur}{\hat{r}}
\newcommand{\ut}{\hat{\theta}}
\setlength{\parskip}{1em}
\fancyhead[L]{Team \teamNumber}
\fancyhead[R]{Page \thepage \hspace{1pt} of \pageref{LastPage}}
%a partir d'aqui es per a ficar el codi maco :)
\usepackage{listings}
\usepackage{color}
\definecolor{dkgreen}{rgb}{0,0.6,0} %canvieu els colors
\definecolor{gray}{rgb}{0.5,0.5,0.5} % pels que us agradin!
\definecolor{mauve}{rgb}{0.58,0,0.82}
\lstset{frame=tb,
aboveskip=3mm,
belowskip=3mm,
showstringspaces=false,
columns=flexible,
basicstyle={\small\ttfamily},
numbers=none,
numberstyle=\tiny\color{gray},
keywordstyle=\color{blue},
commentstyle=\color{dkgreen},
stringstyle=\color{mauve},
breaklines=true,
breakatwhitespace=true,
tabsize=4
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% NO TOCAR LO DE DALT SI NO SABEU QUE FEU :) %
% tocar lo de baix, per a posar les vostres dades!!
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Canviar això per els que toquin al vostre equip
\newcommand{\teamNumber} {744}
\newcommand{\problemLetter} {A}
\title{SOLAR SALES ON YOUR TRIP TO MARS}
\date{} %canviar si voleu data!
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{document}
\begin{titlepage}
\author{Marco Praderio Bova, Eneko Martin Martinez,\\ \& Maria dels Àngels Guinovart Llort \\ Team \# \teamNumber \\ Problem \problemLetter}
\maketitle
\thispagestyle{empty}
\begin{abstract}
\input{abstract.tex}
\end{abstract}
\end{titlepage}
\newpage
\tableofcontents
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%INTRODUCCIO
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newpage
\section{Introduction}
\input{intro.tex}
\newpage
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%OTHER MODELS
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Non Solar Sail models}
\label{sec:nonLinear}
Before starting with the description of our model we will make a brief recap of the most common models used to plan space trajectories in order to achieve a global vision on the matter. The non interested reader skip this section and go straight to section \ref{sec:Model} where we start with our real model. On the other hand for the interested reader we can provide a computer simulation for this models that we had developed before the contest beginning and that can be found in the following github \href{https://github.com/team744UphysicsC/RocketTrajectory}{link}\footnote{https://github.com/team744UphysicsC/RocketTrajectory} that we have created for this sole purpose in order to maintain our identities anonymous as the contest rules require.
\subsection{Hohmann Transfer}
%\input{helio.tex}%posar algo plan deduim les eq del moviment per akest cas que es plan fuel-based i posem tot aixo a l'annex i les equacions les copiem
\input{hohmann.tex}
\subsection{Gravity Assist Encounters}
\input{moonaid.tex}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%MODEL DESCRIPTION
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{The model}
\label{sec:Model}
\subsection{Theoretical introduction}
\subsubsection{Logarithmic Spiral Trajectories}
\input{logarithmic.tex}
\subsubsection{SRP Force}
\input{SRPforces.tex}
\subsubsection{Sun Gravity Force}
\input{gravityforces.tex}
\subsubsection{Differential Equation System}
\input{diffs.tex}
\subsection{Numerical model}
\input{numerical_model.tex}
\newpage
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%RESULTS
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Results}
\input{results.tex}
\newpage
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%FURTHER ANALYSIS
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Further Analysis}
\input{analysis.tex}
\newpage
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%STRENGTHS & WEAKNESSES
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Strengths and Weaknesses}
\input{st_we.tex}
\newpage
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%FUTURE WORK
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Future Work}
\input{backtothefuture.tex}
\section{Conclusions}
\input{conclusions.tex}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% BIBLIOGRAFIA
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newpage
\bibliographystyle{ieeetr}
\bibliography{samples}%les referencies només es mostraran si se'n fa referència per exemple \cite{IntelNode}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%APPENDIX
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newpage
\onecolumn
\newpage
\appendix
\section*{Appendix}
\addcontentsline{toc}{section}{Appendices}
\renewcommand{\thesubsection}{\Alph{subsection}}
%\section{Appendix}
\subsection{Deducing motion equations for Hohmann transfer}
\label{dedueixhohmann}
\input{helio.tex}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%AQUI CODIS!!!
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Codes}
\label{sec:annex}
Codes in Python:
%introduir codi ara és màshic!
\lstinputlisting[language=python]{solar_sailing_to_Mars.py}
\end{document}
```