Started writing finally

LaTeX/thesis.tex

@@ -4,34 +4,122 @@
 \usepackage{mathtools}
 \usepackage{geometry}
 \usepackage{setspace}
+\usepackage{changepage}
+\usepackage{fontspec}
+\usepackage{titlesec}
+
+% \setmainfont{Adamina}
+% \setmainfont{Alegreya}
+\setmainfont[Scale=1.2]{Average}
+
+\titleformat{\section}
+            {\bfseries\fontspec{Roboto}\LARGE}
+            {\thesection}
+            {0.5em}
+            {}
+\titleformat{\subsection}
+            {\fontspec{Roboto}\Large}
+            {\thesubsection}
+            {0.5em}
+            {}
+\titleformat{\subsubsection}
+            {\fontspec{Roboto}\large}
+            {\thesubsubsection}
+            {0.5em}
+            {}
+
+\newcommand{\thesisTitle}{Designing Optimal Low-Thrust Interplanetary Trajectories Utilizing
+Monotonic Basin Hopping}
 
 \geometry{left=1in, right=1in, top=1in, bottom=1in}
 \doublespacing
 
 \begin{document}
 
-  \title{This Will Be The Title Page}
+  \title{\thesisTitle}
-  \author{Richard Connor Johnstone}
+  \author{Richard Connor Johnstone \\
+          B.S., University of Kentucky, 2016}
 
   \maketitle
 
+  \vspace{3.5in}
+
+  \begin{adjustwidth}{100pt}{100pt}
+    \begin{center}
+      A thesis submitted to the Faculty of the Graduate School of the University of Colorado in
+      partial fulfillment of the requirements for the degree of Master of Science Department of
+      Aerospace Engineering Sciences \\ 2022
+    \end{center}
+  \end{adjustwidth}
+
   \newpage
 
   This will be the copyright page.
 
   \newpage
 
-  This will be the signature page.
+  \begin{center}
+    This thesis entitled:
+
+    \thesisTitle
+
+    has been approved for the Department of Aerospace Engineering Sciences
+
+  \end{center}
+
+  \centerline{\begin{minipage}{4in}
+    \begin{center}
+
+      \vspace{1.5in}
+      \hrule
+      Dr. Natasha Bosanac
+
+      \vspace{1.5in}
+      \hrule
+      Dr. Daniel J. Scheeres
+
+      \vspace{1.5in}
+      \hrule
+      Dr. Kathryn Davis
+
+      \vspace{1.5in}
+
+    \end{center}
+  \end{minipage}}
+
+  \hspace{4.25in} Date: \hrulefill
+
+  The final copy of this thesis has been examined by the signatories, and we find that both the
+  content and the form meet acceptable presentation standards of scholarly work in the above
+  mentioned discipline.
 
   \newpage
 
-  This will be the Acknowledgments.
+  %TODO: This should be better
+  Dedicated to some people.
 
   \newpage
 
+  Richard Connor Johnstone
+
+  \thesisTitle
+
+  %TODO: Don't directly copy Bryce's formatting
+  Thesis directed by Dr. Natasha Bosanac
+
+  %TODO: This is just a quick abstract for now. Rewrite more towards the end.
   \begin{abstract}
 
-    This will be the overview/summary/abstract page
+    There are a variety of approaches to finding and optimizing low-thrust trajectories in
+    interplanetary space. This thesis analyzes one such approach, Sims-Flanagan transcriptions, and
+    its applications in a multiple-shooting non-linear solver for the purpose of finding valid
+    low-thrust trajectory arcs between planets given poor initial conditions. These valid arcs are
+    then fed into a Monotonic Basin Hopping (MBH) algorithm, which combines these arcs in order to
+    find and optimize interplanetary trajectories, given a set of flyby planets. This allows for a
+    fairly rapid searching of a very large solution space of low-thrust profiles via a medium
+    fidelity inner-loop solver and a well-suited optimization routine. The trajectories found by
+    this method can then be optimized further by feeding the solutions back, once again, into the
+    non-linear solver, this time allowing the solver to perform optimization. 
 
   \end{abstract}
 
@@ -42,7 +130,16 @@
   \newpage
 
   \section{Introduction}
-    Provide some historical background, motivations, and discussion of the basic problems being investigated. Also a brief overview how the thesis will be laid out.
+
+    Continuous low-thrust arcs utilizing technologies such as Ion propulsion, Halls thrusters, and
+    others can be a powerful tool in the design of space missions. They tend to be particularly
+    suited to missions which require very high total $\Delta V$ values and take place over a
+    particularly long duration. As such, they are well-suited to interplanetary missions. For
+    instance, low thrust ion propulsion was used on the Bepi-Colombo, Dawn, and Deep Space 1
+    missions. 
+
+    Provide some historical background, motivations, and discussion of the basic problems being
+    investigated. Also a brief overview how the thesis will be laid out.
 
   \section{Trajectory Optimization}
     This section will outline the foundational problem of trajectory optimization.
@@ -54,7 +151,8 @@
         Detail Kepler's equations for astrodynamics.
 
     \subsection{Analytical Solutions to Kepler's Equations}
-      Discuss how, since the 2BP is analytically solveable, there exists algorithms for solving these equations.
+      Discuss how, since the 2BP is analytically solveable, there exists algorithms for solving
+      these equations.
 
       \subsubsection{LaGuerre-Conway Algorithm}
         Step through the LaGuerre-Conway algorithm, as it's used in this implementation.
@@ -69,40 +167,50 @@
         Discuss how the Newton Trust-Region method works.
 
       \subsubsection{Linesearch Method}
-        I may take this section out, because I'm not currently using a linesearch. But I would cover the additions of linesearch methods.
+        I may take this section out, because I'm not currently using a linesearch. But I would cover
+        the additions of linesearch methods.
 
   \section{Low-Thrust Considerations}
     Highlight the differences between high and low-thrust mission profiles.
 
     \subsection{Low Thrust Overview}
-      Dive deeper into the concept of low thrust trajectories, highlighting the added trouble with propagation/integration.
+      Dive deeper into the concept of low thrust trajectories, highlighting the added trouble with
+      propagation/integration.
 
     \subsection{Sims-Flanagan Transcription}
-      Reveal the advantages of Sims-Flanagan transcription as an alternative to higher-fidelity propagation models. Be sure to mention its uses in many legitimate places.
+      Reveal the advantages of Sims-Flanagan transcription as an alternative to higher-fidelity
+      propagation models. Be sure to mention its uses in many legitimate places.
 
   \section{Interplanetary Trajectory Considerations}
-    Highlight the problems with the 2BP in co-ordinating influences of extra bodies over an interplanetary journey.
+    Highlight the problems with the 2BP in co-ordinating influences of extra bodies over an
+    interplanetary journey.
 
     \subsection{Patched Conics}
       Describe the method of patched conics.
 
     \subsection{Gravity Assist Maneuvers}
-      Describe how a gravity assist maneuver would work in the framework of patched conics. Also discuss the advantages of such a maneuver.
+      Describe how a gravity assist maneuver would work in the framework of patched conics. Also
+      discuss the advantages of such a maneuver.
 
     \subsection{Multiple Gravity Assist Techniques}
-      Discuss the advantages of chaining together multiple gravity assists and highlight the difficulties in choosing these assists. Here I can mention porkchop plots, Lambert's problem, etc. Here I can also talk about Hybrid Optimal Control Problems.
+      Discuss the advantages of chaining together multiple gravity assists and highlight the
+      difficulties in choosing these assists. Here I can mention porkchop plots, Lambert's problem,
+      etc. Here I can also talk about Hybrid Optimal Control Problems.
 
     \subsection{Ephemeris Considerations}
       I can quickly mention SPICE here and talk a bit about validation.
 
   \section{Genetic Algorithms}
-    I will probably give only a brief overview of genetic algorithms here. I don't personally know that much about them. Then in the following subsections I can discuss the parts that are relevant to the specific algorithm that I'm using.
+    I will probably give only a brief overview of genetic algorithms here. I don't personally know
+    that much about them. Then in the following subsections I can discuss the parts that are
+    relevant to the specific algorithm that I'm using.
 
     \subsection{Decision Vectors}
       Discuss what a decision vector is in the context of an optimization problem.
 
     \subsection{Selection and Fitness Evaluation}
-      Discuss the costing being used as well as the different types of fitness evaluation that are common. Also discuss the concept of generations and ``survival''.
+      Discuss the costing being used as well as the different types of fitness evaluation that are
+      common. Also discuss the concept of generations and ``survival''.
 
       \subsubsection{Tournament Selection}
         Dive deeper into the specific selection algorithm being used here.
@@ -117,34 +225,48 @@
         Discuss both the necessity for mutation and the mutation algorithm being used.
 
   \section{Algorithm Overview}
-    Highlight the algorithm at a high-level. This is likely where flowcharts and diagrams will go to give a high-level overview.
+    Highlight the algorithm at a high-level. This is likely where flowcharts and diagrams will go to
+    give a high-level overview.
 
     \subsection{Trajectory Composition}
-      Discuss briefly the nomenclature used in defining these trajectories. Currently this isn't ``baked in'' to the code, so I have some freedom to adopt Englander's notation or use my own (since my intended use case is a little simpler).
+      Discuss briefly the nomenclature used in defining these trajectories. Currently this isn't
+      ``baked in'' to the code, so I have some freedom to adopt Englander's notation or use my own
+      (since my intended use case is a little simpler).
 
     \subsection{Inner Loop Implementation}
-      Give a better overview of the inner loop specifically. Probably this section will have a more in-depth flowchart.
+      Give a better overview of the inner loop specifically. Probably this section will have a more
+      in-depth flowchart.
 
       \subsubsection{LaGuerre-Conway Kepler Solver}
-        Discuss how the LaGuerre-Conway algorithm is used in the code to provide a fundamental ``natural trajectory'' between two quantized, but not necessarily close points. Mention validation.
+        Discuss how the LaGuerre-Conway algorithm is used in the code to provide a fundamental
+        ``natural trajectory'' between two quantized, but not necessarily close points. Mention
+        validation.
 
       \subsubsection{Sims-Flanagan Propagator}
-        Discuss how this algorithm can then be expanded by using SFT to propagate any number of low-thrust steps over a specific arc. Mention validation. Here I can also mention the ``Sc'' object and talk about how those parameters were chosen and effected the propagator.
+        Discuss how this algorithm can then be expanded by using SFT to propagate any number of
+        low-thrust steps over a specific arc. Mention validation. Here I can also mention the ``Sc''
+        object and talk about how those parameters were chosen and effected the propagator.
 
       \subsubsection{Non-Linear Problem Solver}
-        Mention the package being used to solve NLPs and how it works, highlighting the trust region method used and error-handling. Mention validation.
+        Mention the package being used to solve NLPs and how it works, highlighting the trust region
+        method used and error-handling. Mention validation.
 
       \subsubsection{Monotonic Basin Hopping}
-        Outline the MBH algorithm, going into detail at each step. Mention the long-tailed PDF being used and go into quite a bit of detail. Englander's paper on the MBH algorithm specifically should be a good guide. Mention validation.
+        Outline the MBH algorithm, going into detail at each step. Mention the long-tailed PDF being
+        used and go into quite a bit of detail. Englander's paper on the MBH algorithm specifically
+        should be a good guide. Mention validation.
 
     \subsection{Outer Loop Implementation}
-      Overview the outer loop. This may require a final flowchart, but might potentially be too simple to lend itself to one.
+      Overview the outer loop. This may require a final flowchart, but might potentially be too
+      simple to lend itself to one.
 
       \subsubsection{Inner Loop Calling Function}
         The primary reason for including this section is to discuss the error handling.
 
       \subsubsection{Genetic Algorithm Description}
-        Similar to the MBH section, there are a lot of implementation details to go over here. Many will have already been discussed in the background sections above. But I can step through each of the decisions, similar to Englander's paper on this.
+        Similar to the MBH section, there are a lot of implementation details to go over here. Many
+        will have already been discussed in the background sections above. But I can step through
+        each of the decisions, similar to Englander's paper on this.
 
   \section{Results Analysis}
     Simply highlight that the algorithm was tested on a sample trajectory to Saturn.
@@ -153,23 +275,28 @@
       Give an overview of the trajectory that was ultimately chosen.
 
       \subsubsection{Comparison to Less Optimal Solutions}
-        I should have a number of elite but less-optimal solutions. Honestly, I may write the algorithm to keep all of the solutions to provide many points of comparison here.
+        I should have a number of elite but less-optimal solutions. Honestly, I may write the
+        algorithm to keep all of the solutions to provide many points of comparison here.
 
       \subsubsection{Cost Function Analysis}
         Give some real-world context for the mass-use, time-of-flight, etc.
 
       \subsubsection{Comparison to Impulsive Trajectories}
-        I may also remove this section. I could do a quick comparison (using porkchop plots) to similar impulsive trajectories. Honestly, this is a lot of work for very little gain, though, so probably the first place to chop if needed.
+        I may also remove this section. I could do a quick comparison (using porkchop plots) to
+        similar impulsive trajectories. Honestly, this is a lot of work for very little gain,
+        though, so probably the first place to chop if needed.
 
   \section{Conclusion}
     \subsection{Overview of Results}
       Quick re-wording of the previous section in a paragraph or two for reader's convenience.
 
     \subsection{Applications of Algorithm}
-      Talk a bit about why this work is valuable. Missions that could have benefited, missions that this enables, etc.
+      Talk a bit about why this work is valuable. Missions that could have benefited, missions that
+      this enables, etc.
 
     \subsection{Recommendations for Future Work}
-      Recommend future work, obviously. There are a \emph{ton} of opportunities for improvement including parallelization, cluster computing, etc.
+      Recommend future work, obviously. There are a \emph{ton} of opportunities for improvement
+      including parallelization, cluster computing, etc.
 
   % \bibliography{biblio}{}
   % \bibliographystyle{plain}

Makefile

@@ -18,12 +18,18 @@ $(NOTES_PDFS): $(NOTES)
 		-f markdown  $< \
 		-o $@
 
-$(THESIS_PDF): $(THESIS)
+thesis_pdf/:
+	mkdir $@
+
+$(THESIS_PDF): $(THESIS) thesis_pdf/
 	xelatex $<
-	rm thesis.aux thesis.log thesis.toc
+	xelatex $<
+	mv thesis.* thesis_pdf/
+	cp thesis_pdf/thesis.pdf .
 
 .PHONY: clean
 
 clean:
 	rm -rf $(THESIS_PDF)
 	rm -rf $(NOTES_PDFS)
+	rm -rf thesis_pdf

julia/find_neptune.jl

@@ -55,7 +55,7 @@ end
 
 log(_::Nothing, _::Vector{Mission}, _::Vector{Body}) = println("No Mission Found...")
 
-planets = [Earth, Venus, Mars, Saturn]
+planets = [Earth, Venus, Venus Jupiter, Saturn]
 best, archive = mbh(planets)
 log(best, archive, planets)