Finalized. Wish me luck!

LaTeX/presentation.tex

@@ -35,10 +35,10 @@
 
 	\subsection{Motivation}
 
-		\begin{frame} \frametitle{Motivation}
-			How can we leverage existing technologies and techniques to determine
-			optimally-controlled trajectories to targets in interplanetary space?
-		\end{frame}
+		% \begin{frame} \frametitle{Motivation}
+		% 	How can we leverage existing technologies and techniques to determine
+		% 	optimally-controlled trajectories to targets in interplanetary space?
+		% \end{frame}
 
 		\note{Today I'll be discussing my research in determining optimal trajectories
 		for interplanetary mission objectives. Numerous scientific and engineering advances have
@@ -96,50 +96,17 @@
 		thrust nature changes the underlying system dynamics that would have been used to optimize a
 		mission such as Voyager, which did not employ low-thrust engines.}
 
-		% \begin{frame} \frametitle{Current tools}
-		% 	Indirect Methods:
-		% 	\begin{itemize}
-		% 		\item CHEBYTOP
-		% 		\item NEWSEP
-		% 		\item SEPTOP
-		% 		\item VARITOP
-		% 	\end{itemize}
-
-		% 	Direct Methods:
-		% 	\begin{itemize}
-		% 		\item EMTG
-		% 		\item GALLOP
-		% 		\item MALTO
-		% 		\item PAGMO
-		% 	\end{itemize}
-		% \end{frame}
-
-		% \note{However, many interesting techniques have been developed to combat this issue,
-		% particularly in recent years. A number of different algorithms have been developed  }
-
-	% \subsection{Scope}
-
-		% \begin{frame} \frametitle{First Frame}
-		% 	\begin{itemize}
-		% 		\item Item 1
-		% 		\item Item 2
-		% 	\end{itemize}
-		% \end{frame}
-
-	% \subsection{Problem Statement}
-
-		% \begin{frame} \frametitle{First Frame}
-		% 	\begin{itemize}
-		% 		\item Item 1
-		% 		\item Item 2
-		% 	\end{itemize}
-		% \end{frame}
+		\begin{frame} \frametitle{Problem Statement}
+			For a given low-thrust engine, spacecraft parameters, and planetary flyby selections,
+			what is the optimal control thrusting profile, launch conditions, and flyby parameters
+			to arrive at a target outer planet?
+		\end{frame}
 
 \section{Trajectory Optimization Background}
 
 	\subsection{System Dynamics}
 
-		\begin{frame} \frametitle{Two Body Problem}
+		\begin{frame} \frametitle{Dynamical Model: Two Body Problem}
 			\begin{columns}
 					\begin{column}{0.45\paperwidth}
 						Assumptions:
@@ -167,7 +134,7 @@
 		which it is orbiting. Secondly, both of these bodies are modeled as point masses with
 		constant mass. This removes the need to account for non-uniform densities and asymmetry.}
 
-		\begin{frame} \frametitle{Two Body Problem}
+		\begin{frame} \frametitle{Dynamical Model: Two Body Problem}
 			\begin{columns}
 					\begin{column}{0.45\paperwidth}
 						\begin{align*}
@@ -187,7 +154,7 @@
 		\note{From Newton's second law and the law of universal gravitation, we can then model this
 		force with this equation. Where...}
 
-		\begin{frame} \frametitle{Two Body Problem}
+		\begin{frame} \frametitle{Dynamical Model: Two Body Problem}
 			\begin{columns}
 					\begin{column}{0.45\paperwidth}
 						\begin{equation*}
@@ -206,7 +173,7 @@
 
 		\note{Dividing by the mass, we can derive the acceleration...}
 
-		\begin{frame} \frametitle{Two Body Problem}
+		\begin{frame} \frametitle{Dynamical Model: Two Body Problem}
 			\begin{columns}
 					\begin{column}{0.45\paperwidth}
 						\begin{align*}
@@ -228,7 +195,7 @@
 		parameter as a function of the planetary mass alone, rather than both combined. With this
 		assumption, we can model the system dynamics with this analytically solvable equation}
 
-		\begin{frame} \frametitle{Kepler's Laws}
+		\begin{frame} \frametitle{Dynamical Model: Kepler's Laws}
 			\begin{itemize}
 				\item Each planet's orbit is an ellipse with the Sun at one of the foci.
 				\item The area swept out by the imaginary line connecting the primary and secondary
@@ -241,7 +208,7 @@
 		\note{In the early 1600s, Johannes Kepler determined three laws in order to describe the
 		motion of a satellite. These are:}
 
-		\begin{frame} \frametitle{Kepler's Laws}
+		\begin{frame} \frametitle{Dynamical Model: Kepler's Laws}
 			\begin{equation*}
 				r = \frac{\sfrac{h^2}{\mu}}{1 + e \cos(\theta)}
 			\end{equation*}
@@ -263,7 +230,7 @@
 		actually take them a step further, producing the following extremely useful equations for
 		representing spacecraft motion:}
 
-		\begin{frame} \frametitle{Kepler's Equation}
+		\begin{frame} \frametitle{Dynamical Model: Kepler's Equation}
 			\begin{equation*}
 				\frac{\Delta t}{T} = \frac{E - e \sin E}{2 \pi}
 			\end{equation*}
@@ -295,7 +262,7 @@
 
 	\subsection{Interplanetary Trajectories}
 
-		\begin{frame} \frametitle{Patched Conics}
+		\begin{frame} \frametitle{Interplanetary Trajectories: Patched Conics}
 			\begin{figure}[H]
 				\centering
 				\includegraphics[height=0.7\paperheight]{LaTeX/fig/patched_conics}
@@ -310,7 +277,7 @@
 		sub-trajectories, each governed by a distinct single body when the spacecraft is within the
 		sphere of influence of that particular body...}
 
-		\begin{frame} \frametitle{Gravity Assist}
+		\begin{frame} \frametitle{Interplanetary Trajectories: Gravity Assist}
 			\begin{figure}[H]
 				\centering
 				\includegraphics[height=0.7\paperheight]{LaTeX/fig/flyby}
@@ -326,7 +293,7 @@
 
 	\subsection{Low Thrust Trajectories}
 
-		\begin{frame} \frametitle{Sims-Flanagan Transcription}
+		\begin{frame} \frametitle{Low Thrust Trajectories: Sims-Flanagan Transcription}
 			\begin{columns}
 					\begin{column}{0.45\paperwidth}
 						\begin{itemize}
@@ -351,7 +318,7 @@
 		trajectories with a single impulsive thrust in the center of each. Effectively, this
 		allows...}
 
-		\begin{frame} \frametitle{Control Vector Description}
+		\begin{frame} \frametitle{Low Thrust Trajectories: Control Vector Description}
 			\begin{columns}
 					\begin{column}{0.45\paperwidth}
 						\begin{align*}
@@ -607,6 +574,26 @@
 
 \section{Conclusion}
 
+	\begin{frame} \frametitle{Conclusion}
+		\begin{itemize}
+			\item Validation of direct approach to optimizing interplanetary, low-thrust
+				trajectories as non-linear programming problems
+			\item Validation of Monotonic Basin Hopping algorithm for finding global optima in the
+				same scenario
+			\item Application in a realistic sample mission revealed two effective trajectory
+				possibilities
+		\end{itemize}
+	\end{frame}
+
+	\begin{frame} \frametitle{Future Work}
+		\begin{itemize}
+			\item Outer loop which chooses optimal flyby trajectories for increased automation
+			\item Parallelization would be effective for this problem
+			\item Better quantification of search space ``coverage'' by the monotonic basin hopping
+				algorithm
+		\end{itemize}
+	\end{frame}
+
 	\begin{frame}
 		\begin{center}
 		\begin{Huge}