First draft of presentation
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LaTeX/presentation.bib
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@misc{nasa_voyager,
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title={Voyager - Mission Overview},
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url={https://voyager.jpl.nasa.gov/mission/},
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journal={NASA},
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publisher={NASA}
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}
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@phdthesis{dhanasarCassini,
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author = {Dhanasar, Mookesh},
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year = {2005},
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month = {12},
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||||
pages = {},
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||||
title = {A METHOD FOR THE DESIGN AND ANALYSIS OF DEEP SPACE NUCLEAR PROPULSION SYSTEMS}
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}
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||||
@article{jehnBepi,
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author = {Jehn, Rüdiger and García Yárnoz, Daniel and Schoenmaekers, Johannes and Companys, Vicente},
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year = {2012},
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||||
month = {01},
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||||
pages = {1-9},
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||||
title = {Trajectory Design for BepiColombo Based on Navigation Requirements},
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volume = {4},
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||||
journal = {Journal of Aerospace Engineering, Sciences and Applications},
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||||
doi = {10.7446/jaesa.0401.01}
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||||
}
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@@ -1,25 +1,26 @@
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\documentclass{beamer}
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\title{Designing Optimal Low-Thrust Interplanetary Trajectories}
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||||
\subtitle{Utilizing Monotonic Basin Hopping}
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||||
\title{Designing Optimal Low-Thrust Interplanetary Trajectories Utilizing Monotonic Basin Hopping}
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||||
\author{Richard Connor Johnstone}
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||||
\institute{University of Colorado -- Boulder}
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\date{\today}
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@@ -32,19 +33,589 @@
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\section{Introduction}
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||||
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||||
\begin{frame} \frametitle{First Frame}
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||||
\begin{itemize}
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||||
\item Item 1
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||||
\item Item 2
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||||
\end{itemize}
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\subsection{Motivation}
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||||
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\begin{frame} \frametitle{Motivation}
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How can we leverage existing technologies and techniques to determine
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optimally-controlled trajectories to targets in interplanetary space?
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||||
\end{frame}
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||||
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||||
\note{Today I'll be discussing my research in determining optimal trajectories
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||||
for interplanetary mission objectives. Numerous scientific and engineering advances have
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been made possible by the recognition of optimal trajectories in interplanetary space.}
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||||
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||||
\begin{frame} \frametitle{Voyager}
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||||
\begin{figure}
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||||
\centering
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||||
\includegraphics[height=0.6\paperheight]{LaTeX/fig/voyager}
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||||
\caption{Voyager mission trajectory\cite{nasa_voyager}}
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||||
\end{figure}
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||||
\end{frame}
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||||
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||||
\note{For instance, the Voyagers I and II missions were launched in 1977 because of a
|
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once-in-a-lifetime window in which the spacecraft were able to, on a single tour, visit all
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four gas giant outer planets. These tours were only made possible because of the ability to
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compute planetary ephemeris and map out a chain of gravity assists.}
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||||
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||||
\begin{frame} \frametitle{Bepi-Colombo}
|
||||
\begin{figure}
|
||||
\centering
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||||
\includegraphics[height=0.6\paperheight]{LaTeX/fig/bepicolombo}
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||||
\caption{Bepi-Colombo mission trajectory\cite{jehnBepi}}
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||||
\end{figure}
|
||||
\end{frame}
|
||||
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||||
\note{More recently, ESA has also been able to take advantage of gravity assists to send the
|
||||
spacecraft Bepi-Colombo into a trajectory that rendezvous 6 times with Mercury. While this
|
||||
mission did utilize a number of gravity assists, it also utilized another technology
|
||||
well-suited to interplanetary travel: low-thrust electric propulsion systems}
|
||||
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||||
\subsection{Context}
|
||||
|
||||
\begin{frame} \frametitle{Low Thrust Electric Propulsion}
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||||
Allows for some advantages in achieving more interesting mission objectives:
|
||||
\begin{itemize}
|
||||
\item Much higher thrusting efficiency (in terms of fuel usage) compared to high
|
||||
thrust propulsive systems
|
||||
\item Allows for a greater overall $\Delta V$ budget for a given mission
|
||||
\end{itemize}
|
||||
|
||||
\pause
|
||||
But requires some additional considerations:
|
||||
\begin{itemize}
|
||||
\item Requires significantly more time to achieve the same velocity change
|
||||
\item Defines a new system dynamics control, which must be accounted for
|
||||
continuously at each point in time, requiring additional computation for
|
||||
optimization
|
||||
\end{itemize}
|
||||
\end{frame}
|
||||
|
||||
\note{Thanks to their ability to provide thrust extremely efficiently, these low-thrust
|
||||
engines can be a powerful tool for enabling impressive scientific objectives, but they do
|
||||
provide an additional layer of complexity for the mission designer, as their continuous
|
||||
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}
|
||||
|
||||
\section{Trajectory Optimization Background}
|
||||
|
||||
\subsection{System Dynamics}
|
||||
|
||||
\begin{frame} \frametitle{Two Body Problem}
|
||||
\begin{columns}
|
||||
\begin{column}{0.45\paperwidth}
|
||||
Assumptions:
|
||||
\begin{itemize}
|
||||
\item There are only two bodies in the system
|
||||
\item The only force acting between the two bodies is gravitational
|
||||
\item The two masses are to be modeled as constant point masses
|
||||
\end{itemize}
|
||||
\end{column}
|
||||
\begin{column}{0.45\paperwidth}
|
||||
\begin{figure}
|
||||
\centering
|
||||
\includegraphics[width=0.45\paperwidth]{LaTeX/fig/2bp}
|
||||
\end{figure}
|
||||
\end{column}
|
||||
\end{columns}
|
||||
\end{frame}
|
||||
|
||||
\note{In order to understand how to optimize these trajectories, we'll first have to
|
||||
understand the underlying system dynamics. I won't spend too long on this, as most of you
|
||||
should have a good grasp on spacecraft dynamics, but we'll briefly analyse the most basic
|
||||
model for spaceflight dynamics: the two body problem. This model requires us to make a
|
||||
couple of basic assumptions. First that we are only concerned with the gravitational
|
||||
influence between the nominative two bodies: the spacecraft and the planetary body around
|
||||
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{columns}
|
||||
\begin{column}{0.45\paperwidth}
|
||||
\begin{align*}
|
||||
m_2 \ddot{\vec{r}}_2 &= - \frac{G m_1 m_2}{r^2} \frac{\vec{r}}{\left| r \right|} \\
|
||||
m_1 \ddot{\vec{r}}_1 &= \frac{G m_2 m_1}{r^2} \frac{\vec{r}}{\left| r \right|}
|
||||
\end{align*}
|
||||
\end{column}
|
||||
\begin{column}{0.45\paperwidth}
|
||||
\begin{figure}
|
||||
\centering
|
||||
\includegraphics[width=0.45\paperwidth]{LaTeX/fig/2bp}
|
||||
\end{figure}
|
||||
\end{column}
|
||||
\end{columns}
|
||||
\end{frame}
|
||||
|
||||
\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{columns}
|
||||
\begin{column}{0.45\paperwidth}
|
||||
\begin{equation*}
|
||||
\ddot{\vec{r}} = \ddot{\vec{r}}_2 - \ddot{\vec{r}}_1 =
|
||||
- \frac{G \left( m_1 + m_2 \right)}{r^2} \frac{\vec{r}}{\left| r \right|}
|
||||
\end{equation*}
|
||||
\end{column}
|
||||
\begin{column}{0.45\paperwidth}
|
||||
\begin{figure}
|
||||
\centering
|
||||
\includegraphics[width=0.45\paperwidth]{LaTeX/fig/2bp}
|
||||
\end{figure}
|
||||
\end{column}
|
||||
\end{columns}
|
||||
\end{frame}
|
||||
|
||||
\note{Dividing by the mass, we can derive the acceleration...}
|
||||
|
||||
\begin{frame} \frametitle{Two Body Problem}
|
||||
\begin{columns}
|
||||
\begin{column}{0.45\paperwidth}
|
||||
\begin{align*}
|
||||
\mu &= G (m_1 + m_2) \approx G m_1 \\
|
||||
\ddot{\vec{r}} &= - \frac{\mu}{r^2} \hat{r}
|
||||
\end{align*}
|
||||
\end{column}
|
||||
\begin{column}{0.45\paperwidth}
|
||||
\begin{figure}
|
||||
\centering
|
||||
\includegraphics[width=0.45\paperwidth]{LaTeX/fig/2bp}
|
||||
\end{figure}
|
||||
\end{column}
|
||||
\end{columns}
|
||||
\end{frame}
|
||||
|
||||
\note{Finally, we'll make the assumption that the mass of the spacecraft, is significantly
|
||||
smaller than the mass of the planet. This allows us to represents the gravitational
|
||||
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{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
|
||||
bodies increases linearly with respect to time.
|
||||
\item The square of the orbital period is proportional to the cube of the semi-major
|
||||
axis of the orbit, regardless of eccentricity.
|
||||
\end{itemize}
|
||||
\end{frame}
|
||||
|
||||
\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{equation*}
|
||||
r = \frac{\sfrac{h^2}{\mu}}{1 + e \cos(\theta)}
|
||||
\end{equation*}
|
||||
|
||||
\vspace{1em}
|
||||
|
||||
\begin{equation*}
|
||||
\frac{\Delta t}{T} = \frac{E - e \sin E}{2 \pi}
|
||||
\end{equation*}
|
||||
|
||||
\vspace{1em}
|
||||
|
||||
\begin{equation*}
|
||||
T = 2 \pi \sqrt{\frac{a^3}{\mu}}
|
||||
\end{equation*}
|
||||
\end{frame}
|
||||
|
||||
\note{By utilizing these laws and some geometric properties of conic sections, we can
|
||||
actually take them a step further, producing the following extremely useful equations for
|
||||
representing spacecraft motion:}
|
||||
|
||||
\begin{frame} \frametitle{Kepler's Equation}
|
||||
\begin{equation*}
|
||||
\frac{\Delta t}{T} = \frac{E - e \sin E}{2 \pi}
|
||||
\end{equation*}
|
||||
|
||||
\vspace{1em}
|
||||
|
||||
\begin{equation*}
|
||||
T = 2 \pi \sqrt{\frac{a^3}{\mu}}
|
||||
\end{equation*}
|
||||
|
||||
\vspace{1em}
|
||||
|
||||
\begin{equation*}
|
||||
M = \sqrt{\frac{\mu}{a^3}} \Delta t = E - e \sin E
|
||||
\end{equation*}
|
||||
\end{frame}
|
||||
|
||||
\note{The second of these, which we'll take particular notice of, is considered Kepler's
|
||||
equation. It provides a method for relating the time since periapsis of a satellite in an
|
||||
orbit to the satellite's position along that orbit. The solution to this equatin can then be
|
||||
used to solve for a spacecraft's position, which is very useful for direct optimization
|
||||
methods.}
|
||||
|
||||
% \note{Finally, though, we'll need to actually solve Kepler's equation. For this purpose
|
||||
% we'll use a generic root-finding method first proposed by Laguerre in the 19th century.
|
||||
% Conway first explored its application on Kepler's equation in the 1980s and found it to be
|
||||
% more robust at converging to a solution, with similar convergence speed, to the more common
|
||||
% variations of the Newton-Raphson method}
|
||||
|
||||
\subsection{Interplanetary Trajectories}
|
||||
|
||||
\begin{frame} \frametitle{Patched Conics}
|
||||
\begin{figure}[H]
|
||||
\centering
|
||||
\includegraphics[height=0.7\paperheight]{LaTeX/fig/patched_conics}
|
||||
\end{figure}
|
||||
\end{frame}
|
||||
|
||||
\note{Now that we have a grasp on the underlying system dynamics, we can consider the
|
||||
additions needed for interplanetary travel specifically. To this end, we'll consider the
|
||||
method of patched conics, a technique for reconciling the fact that the spacecraft will not
|
||||
be under the influence of a single body, but actually a number of different bodies over the
|
||||
course of its trajectory. To achieve this, we'll break the trajectory up into different
|
||||
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{figure}[H]
|
||||
\centering
|
||||
\includegraphics[height=0.7\paperheight]{LaTeX/fig/flyby}
|
||||
\end{figure}
|
||||
\end{frame}
|
||||
|
||||
\note{You'll notice, though, that the trajectories within the sphere of influence aren't
|
||||
elliptical orbits. They're hyperbolic. Because of this fact, we can take advantage of the
|
||||
gravity flyby effect. Because of the nature of the hyperbolic arc the spacecraft takes
|
||||
around the planet, the spacecraft leaves in a different direction than it arrives. This
|
||||
effect can be targeted up to a point, and a free "maneuver" can be achieved, changing the
|
||||
direction of the spacecraft's motion relative to the Sun.}
|
||||
|
||||
\subsection{Low Thrust Trajectories}
|
||||
|
||||
\begin{frame} \frametitle{Sims-Flanagan Transcription}
|
||||
\begin{columns}
|
||||
\begin{column}{0.45\paperwidth}
|
||||
\begin{itemize}
|
||||
\item Each trajectory broken into $n$ segments
|
||||
\item Impulsive thrust at the center of each one, assuming equal thrust
|
||||
over the segment
|
||||
\item Mass decremented over the duration of the segment
|
||||
\end{itemize}
|
||||
\end{column}
|
||||
\begin{column}{0.45\paperwidth}
|
||||
\begin{figure}
|
||||
\centering
|
||||
\includegraphics[width=0.45\paperwidth]{LaTeX/fig/sft}
|
||||
\end{figure}
|
||||
\end{column}
|
||||
\end{columns}
|
||||
\end{frame}
|
||||
|
||||
\note{We'll also need to discretize the low-thrust controls in order to apply a direct
|
||||
optimization. This is achieved, in this thesis and many other implementations, with the
|
||||
Sims-Flanagan transcription. The trajectory is broken up into a number of smaller
|
||||
trajectories with a single impulsive thrust in the center of each. Effectively, this
|
||||
allows...}
|
||||
|
||||
\begin{frame} \frametitle{Control Vector Description}
|
||||
\begin{columns}
|
||||
\begin{column}{0.45\paperwidth}
|
||||
\begin{align*}
|
||||
F_r &= F \cos(\beta) \sin (\alpha) \\
|
||||
F_\theta &= F \cos(\beta) \cos (\alpha) \\
|
||||
F_h &= F \sin(\beta)
|
||||
\end{align*}
|
||||
\end{column}
|
||||
\begin{column}{0.45\paperwidth}
|
||||
\begin{figure}
|
||||
\centering
|
||||
\includegraphics[width=0.45\paperwidth]{LaTeX/fig/thrust_angle}
|
||||
\end{figure}
|
||||
\end{column}
|
||||
\end{columns}
|
||||
\end{frame}
|
||||
|
||||
\note{Finally, in order to better understand the thrust control vector, we need a useful
|
||||
frame. For this purpose, I use the r theta h frame in which the r axis is... This is useful
|
||||
because the theta axis is aligned fairly close to the velocity direction. That allows for a
|
||||
useful framework in which to analyze the control thrusts. Thrusts with a low alpha angle are
|
||||
useful for raising the energy of the orbit, while other thrusts (either alpha around pi/2 or
|
||||
high beta) are useful for steering controls.}
|
||||
|
||||
\section{Algorithm Overview}
|
||||
|
||||
\subsection{Trajectory Composition}
|
||||
|
||||
\begin{frame} \frametitle{Input Description}
|
||||
\footnotesize{
|
||||
\begin{itemize}
|
||||
\item \textbf<1>{Spacecraft dry mass in kilograms}
|
||||
\item \textbf<1>{Total starting mass of the Spacecraft in kilograms}
|
||||
\item \textbf<2>{Thruster Specific Impulse in seconds}
|
||||
\item \textbf<2>{Thruster Maximum Thrusting Force in Newtons}
|
||||
\item \textbf<2>{Thruster Duty Cycle Percentage}
|
||||
\item \textbf<2>{Number of Thrusters on Spacecraft}
|
||||
\item \textbf<3>{The Launch Window Boundaries}
|
||||
\item \textbf<3>{The Latest Arrival Date}
|
||||
\item \textbf<4>{A Maximum Acceptable $V_\infty$ at arrival in kilometers per
|
||||
second}
|
||||
\item \textbf<4>{A Maximum Acceptable $C_3$ at launch in kilometers per second
|
||||
squared}
|
||||
\item \textbf<4>{A cost function relating the mass usage, $v_\infty$ at arrival, and
|
||||
$C_3$ at launch to a cost}
|
||||
\item \textbf<5>{A list of flyby planets starting with Earth and ending with the
|
||||
destination}
|
||||
\end{itemize}
|
||||
}
|
||||
\end{frame}
|
||||
|
||||
\note{In order to fully understand the optimization algorithm, it makes sense to first
|
||||
understand the variables that won't be optimized. These will represent the mission
|
||||
parameters used as inputs to the algorithm. These first two will essentially size the
|
||||
spacecraft that we'll be using. Then the next groups will define the thrusters, the launch
|
||||
and arrival windows, the cost function to be used by the direct optimizer, and finally the
|
||||
flybys that the spacecraft will leverage on its trajectory.}
|
||||
|
||||
\subsection{Inner Loop Implementation}
|
||||
|
||||
\begin{frame} \frametitle{Non-Linear Programming Approach - Definition}
|
||||
A Non-Linear Programming Problem involves finding a solution that optimizes a function:
|
||||
|
||||
\begin{equation*}
|
||||
f(\vec{x})
|
||||
\end{equation*}
|
||||
|
||||
Subject to constraints:
|
||||
\begin{align*}
|
||||
\vec{g}(\vec{x}) &\le 0 \\
|
||||
\vec{h}(\vec{x}) &= 0
|
||||
\end{align*}
|
||||
|
||||
\end{frame}
|
||||
|
||||
\note{Now we'll treat the trajectory as a direct non-linear programming optimization
|
||||
problem. This provides a general approach to determining a local optima to a scalar function
|
||||
f of a vector-valued input, x, subject to constraints g and h, defined as can be seen here.}
|
||||
|
||||
\begin{frame} \frametitle{Non-Linear Programming Approach - Input Vector}
|
||||
\begin{figure}
|
||||
\centering
|
||||
\includegraphics[height=0.7\paperheight]{LaTeX/flowcharts/nlp}
|
||||
\end{figure}
|
||||
\end{frame}
|
||||
|
||||
\note{So we need simply to define the function, constraints, and the input vector. Starting
|
||||
with the input vector, we need to determine...}
|
||||
|
||||
\begin{frame} \frametitle{Non-Linear Programming Approach - Constraints}
|
||||
\begin{itemize}
|
||||
\item For every phase other than the final:
|
||||
\begin{itemize}
|
||||
\item The minimum periapsis of the hyperbolic flyby arc must be above some
|
||||
user-specified minimum safe altitude.
|
||||
\item The magnitude of the incoming hyperbolic velocity must match the magnitude
|
||||
of the outgoing hyperbolic velocity.
|
||||
\item The spacecraft position must match the planet's position (within bounds)
|
||||
at the end of the phase.
|
||||
\end{itemize}
|
||||
\item For the final phase:
|
||||
\begin{itemize}
|
||||
\item The spacecraft position must match the planet's position (within bounds)
|
||||
at the end of the phase.
|
||||
\item The final mass must be greater than the dry mass of the craft.
|
||||
\end{itemize}
|
||||
\end{itemize}
|
||||
\end{frame}
|
||||
|
||||
\note{And we can also determine a series of constraints...}
|
||||
|
||||
\begin{frame} \frametitle{Non-Linear Programming Approach - Cost Function}
|
||||
\begin{equation*}
|
||||
J(\vec{x}, m_{dry}, C_{3,max}) = 3 \left| \frac{m(\vec{x})}{m_{dry}} \right| +
|
||||
\left| \frac{C_3(\vec{x})}{C_{3,max}} \right|
|
||||
\end{equation*}
|
||||
\end{frame}
|
||||
|
||||
\note{Finally, the cost function was designed to be user-specified. However, for the
|
||||
implementation of this particular project, I utilized a combination of the normalized fuel
|
||||
usage and launch c3. Now we have a fully-defined non-linear programming problem that can be
|
||||
optimized using any direct method optimization scheme.}
|
||||
|
||||
\subsection{Outer Loop Implementation}
|
||||
|
||||
\begin{frame} \frametitle{Monotonic Basin Hopping}
|
||||
\begin{figure}
|
||||
\centering
|
||||
\includegraphics[height=0.7\textheight]{LaTeX/flowcharts/mbh}
|
||||
\end{figure}
|
||||
\end{frame}
|
||||
|
||||
\note{Now we have a method for finding local optima in the vicinity of an input vector, but
|
||||
what we're after is the global optima, meaning that we need a method for testing a variety
|
||||
of input vectors, each of which could either fail to produce a valid trajectory after the
|
||||
inner loop or produce a valid solution that may or may not be in a "basin", or collection of
|
||||
nearby valid solutions with a single "regional" optimum. In order to approach this problem,
|
||||
I've employed a Monotonic Basin Hopping algorithm. (Step through each of the steps)}
|
||||
|
||||
\begin{frame} \frametitle{Monotonic Basin Hopping - Perturbation PDF}
|
||||
Pareto Distribution:
|
||||
\begin{equation*}
|
||||
1 +
|
||||
\left[ \frac{s}{\epsilon} \right] \cdot
|
||||
\left[ \frac{\alpha - 1}{\frac{\epsilon}{\epsilon + r}^{-\alpha}} \right]
|
||||
\end{equation*}
|
||||
\end{frame}
|
||||
|
||||
\section{Sample Mission Analysis}
|
||||
|
||||
\subsection{Mission Scenario}
|
||||
|
||||
\begin{frame} \frametitle{Mission Scenario}
|
||||
\begin{itemize}
|
||||
\item Spacecraft starting mass: 3500 kg
|
||||
\item Thruster Specific Impulse: 3200 s
|
||||
\item Thruster Maximum Thrusting Force: 250 mN
|
||||
\item Thruster Duty Cycle: 100\%
|
||||
\item Number of Thrusters: 1
|
||||
\item The Launch Window: 2023 and 2024
|
||||
\item The Latest Arrival Date: December 31st, 2044
|
||||
\item Maximum $C_3$ at launch: $100 \frac{\text{km}^2}{\text{s}^2}$
|
||||
\end{itemize}
|
||||
\end{frame}
|
||||
|
||||
\begin{frame} \frametitle{Flybys Analyzed}
|
||||
\begin{itemize}
|
||||
\item EJS
|
||||
\item EMJS
|
||||
\item EMMJS
|
||||
\item EMS
|
||||
\item ES
|
||||
\item EVMJS
|
||||
\item EVMS
|
||||
\item EVVJS
|
||||
\end{itemize}
|
||||
\end{frame}
|
||||
|
||||
\subsection{Trajectory 1}
|
||||
|
||||
\begin{frame} \frametitle{Trajectory 1 - Earth → Mars → Saturn}
|
||||
\begin{figure}
|
||||
\includegraphics<1>[height=0.5\paperheight]{LaTeX/fig/EMS_plot}
|
||||
\includegraphics<2>[height=0.5\paperheight]{LaTeX/fig/EMS_plot_noplanets}
|
||||
\includegraphics<3>[height=0.5\paperheight]{LaTeX/fig/EMS_thrust_mag}
|
||||
\includegraphics<4>[height=0.5\paperheight]{LaTeX/fig/EMS_thrust_components_vnb}
|
||||
\end{figure}
|
||||
\vspace{-1em}
|
||||
\begin{table}\begin{tiny}
|
||||
\begin{tabular}{ | c c c c c c | }
|
||||
\hline
|
||||
\bfseries Flyby Selection &
|
||||
\bfseries Launch Date &
|
||||
\bfseries Mission Length &
|
||||
\bfseries Launch $C_3$ &
|
||||
\bfseries Arrival $V_\infty$ &
|
||||
\bfseries Fuel Usage \\
|
||||
& & (years) & $\left( \frac{km}{s} \right)^2$ & ($\frac{km}{s}$) & (kg) \\
|
||||
\hline
|
||||
EMS & 2024-06-27 & 7.9844 & 60.41025 & 5.816058 & 446.9227 \\
|
||||
\hline
|
||||
\end{tabular}
|
||||
\end{tiny}\end{table}
|
||||
\end{frame}
|
||||
|
||||
\subsection{Trajectory 2}
|
||||
|
||||
\begin{frame} \frametitle{Trajectory 2 - Earth → Mars → Jupiter → Saturn}
|
||||
\begin{figure}
|
||||
\includegraphics<1>[height=0.5\paperheight]{LaTeX/fig/EMJS_plot}
|
||||
\includegraphics<2>[height=0.5\paperheight]{LaTeX/fig/EMJS_plot_noplanets}
|
||||
\includegraphics<3>[height=0.5\paperheight]{LaTeX/fig/EMJS_thrust_mag}
|
||||
\includegraphics<4>[height=0.5\paperheight]{LaTeX/fig/EMJS_thrust_components_vnb}
|
||||
\end{figure}
|
||||
\vspace{-1em}
|
||||
\begin{table}\begin{tiny}
|
||||
\begin{tabular}{ | c c c c c c | }
|
||||
\hline
|
||||
\bfseries Flyby Selection &
|
||||
\bfseries Launch Date &
|
||||
\bfseries Mission Length &
|
||||
\bfseries Launch $C_3$ &
|
||||
\bfseries Arrival $V_\infty$ &
|
||||
\bfseries Fuel Usage \\
|
||||
& & (years) & $\left( \frac{km}{s} \right)^2$ & ($\frac{km}{s}$) & (kg) \\
|
||||
\hline
|
||||
EMJS & 2023-11-08 & 14.1072 & 40.43862 & 3.477395 & 530.6683 \\
|
||||
\hline
|
||||
\end{tabular}
|
||||
\end{tiny}\end{table}
|
||||
\end{frame}
|
||||
|
||||
\subsection{Results Analysis}
|
||||
|
||||
\begin{frame} \frametitle{Results Review}
|
||||
\begin{table}\begin{tiny}
|
||||
\begin{tabular}{ | c c c c c c | }
|
||||
\hline
|
||||
\bfseries Flyby Selection &
|
||||
\bfseries Launch Date &
|
||||
\bfseries Mission Length &
|
||||
\bfseries Launch $C_3$ &
|
||||
\bfseries Arrival $V_\infty$ &
|
||||
\bfseries Fuel Usage \\
|
||||
& & (years) & $\left( \frac{km}{s} \right)^2$ & ($\frac{km}{s}$) & (kg) \\
|
||||
\hline
|
||||
EMS & 2024-06-27 & 7.9844 & 60.41025 & 5.816058 & 446.9227 \\
|
||||
EMJS & 2023-11-08 & 14.1072 & 40.43862 & 3.477395 & 530.6683 \\
|
||||
\hline
|
||||
\end{tabular}
|
||||
\end{tiny}\end{table}
|
||||
\end{frame}
|
||||
|
||||
\section{Conclusion}
|
||||
|
||||
\begin{frame}
|
||||
\begin{center}
|
||||
\begin{Huge}
|
||||
Thank You!
|
||||
\end{Huge}
|
||||
\end{center}
|
||||
\end{frame}
|
||||
|
||||
\section{Introduction}
|
||||
|
||||
\section{Introduction}
|
||||
|
||||
\section{Introduction}
|
||||
|
||||
\section{Introduction}
|
||||
\bibliographystyle{plain}
|
||||
\bibliography{LaTeX/presentation}
|
||||
|
||||
\end{document}
|
||||
|
||||
5
Makefile
5
Makefile
@@ -2,7 +2,7 @@ SRC_DIR = LaTeX/
|
||||
THESIS_SRC_NAMES = thesis.tex thesis.bib approach.tex conclusion.tex introduction.tex \
|
||||
results.tex trajectory_design.tex trajectory_optimization.tex
|
||||
THESIS_SRC = $(addprefix $(SRC_DIR)/,$(THESIS_SRC_NAMES))
|
||||
THESIS_PRES_SRC_NAMES = presentation.tex
|
||||
THESIS_PRES_SRC_NAMES = presentation.tex presentation.bib
|
||||
THESIS_PRES_SRC = $(addprefix $(SRC_DIR)/,$(THESIS_PRES_SRC_NAMES))
|
||||
THESIS_PRES = presentation.pdf
|
||||
THESIS_PDF = thesis.pdf
|
||||
@@ -21,6 +21,9 @@ $(BUILD_DIR)/$(THESIS_PDF): $(BUILD_DIR) $(THESIS_SRC)
|
||||
|
||||
$(BUILD_DIR)/$(THESIS_PRES): $(BUILD_DIR) $(THESIS_PRES_SRC)
|
||||
xelatex --output-directory $(BUILD_DIR) $(SRC_DIR)/presentation
|
||||
bibtex $(BUILD_DIR)/presentation
|
||||
xelatex --output-directory $(BUILD_DIR) $(SRC_DIR)/presentation
|
||||
xelatex --output-directory $(BUILD_DIR) $(SRC_DIR)/presentation
|
||||
|
||||
$(THESIS_PDF): $(BUILD_DIR)/$(THESIS_PDF)
|
||||
cp $(BUILD_DIR)/thesis.pdf .
|
||||
|
||||
@@ -64,22 +64,22 @@ println(get_id.(sorted_missions2[1:5]))
|
||||
# camera=((-0.2, -0.3, -0.2),(1.75,-1.75,1.5))));
|
||||
|
||||
# Save Orbit Plot
|
||||
savefig(Thesis.plot(short, title="EMS Mission Profile", mode="light", planet_colors=false,
|
||||
phase_colors=["#F00","#F0F","#6AF"], markers=false, legend=false,
|
||||
camera=((-0.2, 0.1, -0.3),(-2.,-2.,1.))),
|
||||
"/home/connor/projects/thesis/LaTeX/fig/EMS_plot.png",
|
||||
width=850, height=400)
|
||||
savefig(Thesis.plot(short, title="EMS Mission Profile", mode="light", planet_colors=false,
|
||||
phase_colors=["#F00","#F0F","#6AF"], markers=false, planets=false, legend=false,
|
||||
camera=((-0.2, 0.1, -0.3),(-2.,-2.,1.))),
|
||||
"/home/connor/projects/thesis/LaTeX/fig/EMS_plot_noplanets.png",
|
||||
width=850, height=400)
|
||||
savefig(Thesis.plot(long, title="EMS Mission Profile", mode="light", planet_colors=false,
|
||||
# savefig(Thesis.plot(short, title="EMS Mission Profile", mode="light", planet_colors=false,
|
||||
# phase_colors=["#F00","#F0F","#6AF"], markers=false, legend=false,
|
||||
# camera=((-0.2, 0.1, -0.3),(-2.,-2.,1.))),
|
||||
# "/home/connor/projects/thesis/LaTeX/fig/EMS_plot.png",
|
||||
# width=850, height=400)
|
||||
# savefig(Thesis.plot(short, title="EMS Mission Profile", mode="light", planet_colors=false,
|
||||
# phase_colors=["#F00","#F0F","#6AF"], markers=false, planets=false, legend=false,
|
||||
# camera=((-0.2, 0.1, -0.3),(-2.,-2.,1.))),
|
||||
# "/home/connor/projects/thesis/LaTeX/fig/EMS_plot_noplanets.png",
|
||||
# width=850, height=400)
|
||||
savefig(Thesis.plot(long, title="EMJS Mission Profile", mode="light", planet_colors=false,
|
||||
phase_colors=["#F00","#F0F","#6AF"], markers=false, legend=false,
|
||||
camera=((-0.2, -0.3, -0.2),(1.75,-1.75,1.5))),
|
||||
"/home/connor/projects/thesis/LaTeX/fig/EMJS_plot.png",
|
||||
width=850, height=400)
|
||||
savefig(Thesis.plot(long, title="EMS Mission Profile", mode="light", planet_colors=false,
|
||||
savefig(Thesis.plot(long, title="EMJS Mission Profile", mode="light", planet_colors=false,
|
||||
phase_colors=["#F00","#F0F","#6AF"], markers=false, planets=false, legend=false,
|
||||
camera=((-0.2, -0.3, -0.2),(2.,-2.,1.5))),
|
||||
"/home/connor/projects/thesis/LaTeX/fig/EMJS_plot_noplanets.png",
|
||||
@@ -89,18 +89,22 @@ savefig(Thesis.plot(long, title="EMS Mission Profile", mode="light", planet_colo
|
||||
# display(plot_thrust_components(display_mission, title="Thrust Components vs Time", mode="light"))
|
||||
|
||||
# Save Thrust Plots
|
||||
savefig(plot_thrust(short, title="Thrust Magnitude vs Time", mode="light", legend=false),
|
||||
"/home/connor/projects/thesis/LaTeX/fig/EMS_thrust_mag.png",
|
||||
width=850, height=400)
|
||||
savefig(plot_thrust_components(short, title="Thrust Components vs Time", mode="light", legend=false),
|
||||
"/home/connor/projects/thesis/LaTeX/fig/EMS_thrust_components.png",
|
||||
width=850, height=400)
|
||||
savefig(plot_thrust(long, title="Thrust Magnitude vs Time", mode="light", legend=false),
|
||||
"/home/connor/projects/thesis/LaTeX/fig/EMJS_thrust_mag.png",
|
||||
width=850, height=400)
|
||||
savefig(plot_thrust_components(long, title="Thrust Components vs Time", mode="light", legend=false),
|
||||
"/home/connor/projects/thesis/LaTeX/fig/EMJS_thrust_components.png",
|
||||
width=850, height=400)
|
||||
# savefig(plot_thrust(short, title="Thrust Magnitude vs Time", mode="light", legend=false),
|
||||
# "/home/connor/projects/thesis/LaTeX/fig/EMS_thrust_mag.png",
|
||||
# width=850, height=400)
|
||||
# savefig(plot_thrust_components(short, title="Thrust Components vs Time", mode="light", legend=false),
|
||||
# "/home/connor/projects/thesis/LaTeX/fig/EMS_thrust_components.png",
|
||||
# width=850, height=400)
|
||||
# savefig(plot_thrust(long, title="Thrust Magnitude vs Time", mode="light", legend=false),
|
||||
# "/home/connor/projects/thesis/LaTeX/fig/EMJS_thrust_mag.png",
|
||||
# width=850, height=400)
|
||||
# savefig(plot_thrust_components(long, title="Thrust Components vs Time", mode="light", legend=false),
|
||||
# "/home/connor/projects/thesis/LaTeX/fig/EMJS_thrust_components.png",
|
||||
# width=850, height=400)
|
||||
|
||||
# Save Thrust Plots (VNB)
|
||||
# display(plot_thrust_components(short, title="Thrust Components vs Time", mode="light", vnb=true))
|
||||
# display(plot_thrust_components(long, title="Thrust Components vs Time", mode="light", vnb=true))
|
||||
|
||||
# Save mission
|
||||
# store(display_mission, "/home/connor/projects/thesis/archive/best/long_mission")
|
||||
|
||||
@@ -1,4 +1,15 @@
|
||||
export oe_to_rθh, rθh_to_xyz, oe_to_xyz, xyz_to_oe, xyz_to_rθh, conv_T, spiral, gen_orbit
|
||||
export oe_to_rθh, rθh_to_xyz, oe_to_xyz, xyz_to_oe, xyz_to_rθh, xyz_to_vnb, conv_T, spiral, gen_orbit
|
||||
|
||||
function xyz_to_vnb(vec::Vector, rv::Vector)
|
||||
r = rv[1:3]
|
||||
v = rv[4:6]
|
||||
h = cross(r,v)
|
||||
n_hat = h/norm(h)
|
||||
v_hat = v/norm(v)
|
||||
b = cross(h,v)
|
||||
b_hat = b/norm(b)
|
||||
return [ dot(vec,v_hat), dot(vec,n_hat), dot(vec,b_hat) ]
|
||||
end
|
||||
|
||||
function oe_to_rθh(oe::Vector,μ::Real) :: Vector
|
||||
|
||||
|
||||
@@ -481,30 +481,32 @@ end
|
||||
function plot_thrust_components(m::Union{Mission, Mission_Guess};
|
||||
title::String="Mission Plot",
|
||||
mode::String="dark",
|
||||
legend=true,
|
||||
vnb=false,
|
||||
)
|
||||
traces = Vector{PlotlyJS.AbstractTrace}()
|
||||
times = Vector{String}()
|
||||
xs = Vector{Float64}()
|
||||
ys = Vector{Float64}()
|
||||
zs = Vector{Float64}()
|
||||
αs = Vector{Float64}()
|
||||
βs = Vector{Float64}()
|
||||
comps1 = Vector{Float64}()
|
||||
comps2 = Vector{Float64}()
|
||||
comps3 = Vector{Float64}()
|
||||
time = datetime2julian(m.launch_date)
|
||||
start = state(Earth, time, m.launch_v∞, m.start_mass)
|
||||
for phase in m.phases
|
||||
n = size(phase.thrust_profile)[1]
|
||||
path = prop(phase.thrust_profile, start, m.sc, phase.tof)
|
||||
for i in 1:n
|
||||
push!(times, format(julian2datetime(time + i*phase.tof/(86400n)),"yyyy-mm-dd HH:MM:SS"))
|
||||
push!(xs, phase.thrust_profile[i,1])
|
||||
push!(ys, phase.thrust_profile[i,2])
|
||||
push!(zs, phase.thrust_profile[i,3])
|
||||
r, θ, h = xyz_to_rθh(phase.thrust_profile[i,1:3], xyz_to_oe(path[i+1,1:6],Sun.μ))
|
||||
β = asin(h)
|
||||
α = atan(r/cos(β),θ/cos(β))
|
||||
push!(αs, α)
|
||||
push!(βs, β)
|
||||
if !vnb
|
||||
push!(times, format(julian2datetime(time + i*phase.tof/(86400n)),"yyyy-mm-dd HH:MM:SS"))
|
||||
fr, fθ, fh = xyz_to_rθh(phase.thrust_profile[i,1:3], xyz_to_oe(path[i+1,1:6],Sun.μ))
|
||||
push!(comps1, fθ)
|
||||
push!(comps2, fh)
|
||||
push!(comps3, fr)
|
||||
else
|
||||
push!(times, format(julian2datetime(time + i*phase.tof/(86400n)),"yyyy-mm-dd HH:MM:SS"))
|
||||
fv, fn, fb = xyz_to_vnb(phase.thrust_profile[i,1:3], path[i+1,1:6])
|
||||
push!(comps1, fv)
|
||||
push!(comps2, fn)
|
||||
push!(comps3, fb)
|
||||
end
|
||||
end
|
||||
time += phase.tof/86400.
|
||||
time_string = format(julian2datetime(time),"yyyy-mm-dd HH:MM:SS")
|
||||
@@ -512,21 +514,23 @@ function plot_thrust_components(m::Union{Mission, Mission_Guess};
|
||||
y=[-10.0,10.0],
|
||||
mode="lines",
|
||||
line_color="#000",
|
||||
name=phase.planet.name*" Flyby"))
|
||||
name=phase.planet.name*" Flyby",
|
||||
showlegend=false))
|
||||
mass = path[end,end]
|
||||
start = state(phase.planet, time, phase.v∞_out, mass)
|
||||
end
|
||||
push!(traces, scatter(;x=times, y=αs, name="in-plane angle"))
|
||||
push!(traces, scatter(;x=times, y=βs, name="out-of-plane angle"))
|
||||
push!(traces, scatter(;x=times, y=comps1, name="velocity component"))
|
||||
push!(traces, scatter(;x=times, y=comps2, name="out of plane component"))
|
||||
push!(traces, scatter(;x=times, y=comps3, name="cross-track component"))
|
||||
|
||||
# Determine layout details
|
||||
layout = Layout(;title=title,
|
||||
xaxis_title="Year",
|
||||
yaxis_title="Thrust Angle (Radians)",
|
||||
yaxis_range=[min(minimum(αs),minimum(βs))*1.02,max(maximum(αs),maximum(βs))*1.02],
|
||||
)
|
||||
|
||||
layout["showlegend"] = legend
|
||||
yaxis_range=[minimum(minimum.([comps1, comps2, comps3]))*1.02,
|
||||
maximum(maximum.([comps1, comps2, comps3]))*1.02],
|
||||
legend_orientation="h",
|
||||
)
|
||||
|
||||
# Plot
|
||||
PlotlyJS.plot( PlotlyJS.Plot( traces, layout ) )
|
||||
|
||||
13
temp/presentation.bbl
Normal file
13
temp/presentation.bbl
Normal file
@@ -0,0 +1,13 @@
|
||||
\begin{thebibliography}{1}
|
||||
|
||||
\bibitem{nasa_voyager}
|
||||
Voyager - mission overview.
|
||||
|
||||
\bibitem{jehnBepi}
|
||||
Rüdiger Jehn, Daniel García~Yárnoz, Johannes Schoenmaekers, and Vicente
|
||||
Companys.
|
||||
\newblock Trajectory design for bepicolombo based on navigation requirements.
|
||||
\newblock {\em Journal of Aerospace Engineering, Sciences and Applications},
|
||||
4:1--9, 01 2012.
|
||||
|
||||
\end{thebibliography}
|
||||
48
temp/presentation.blg
Normal file
48
temp/presentation.blg
Normal file
@@ -0,0 +1,48 @@
|
||||
This is BibTeX, Version 0.99d (TeX Live 2021/Arch Linux)
|
||||
Capacity: max_strings=200000, hash_size=200000, hash_prime=170003
|
||||
The top-level auxiliary file: temp//presentation.aux
|
||||
The style file: plain.bst
|
||||
Database file #1: LaTeX/presentation.bib
|
||||
Warning--to sort, need author or key in nasa_voyager
|
||||
You've used 2 entries,
|
||||
2118 wiz_defined-function locations,
|
||||
508 strings with 4311 characters,
|
||||
and the built_in function-call counts, 514 in all, are:
|
||||
= -- 44
|
||||
> -- 24
|
||||
< -- 0
|
||||
+ -- 10
|
||||
- -- 8
|
||||
* -- 36
|
||||
:= -- 85
|
||||
add.period$ -- 4
|
||||
call.type$ -- 2
|
||||
change.case$ -- 10
|
||||
chr.to.int$ -- 0
|
||||
cite$ -- 3
|
||||
duplicate$ -- 18
|
||||
empty$ -- 46
|
||||
format.name$ -- 8
|
||||
if$ -- 107
|
||||
int.to.chr$ -- 0
|
||||
int.to.str$ -- 2
|
||||
missing$ -- 1
|
||||
newline$ -- 11
|
||||
num.names$ -- 2
|
||||
pop$ -- 13
|
||||
preamble$ -- 1
|
||||
purify$ -- 8
|
||||
quote$ -- 0
|
||||
skip$ -- 17
|
||||
stack$ -- 0
|
||||
substring$ -- 19
|
||||
swap$ -- 2
|
||||
text.length$ -- 0
|
||||
text.prefix$ -- 0
|
||||
top$ -- 0
|
||||
type$ -- 8
|
||||
warning$ -- 1
|
||||
while$ -- 3
|
||||
width$ -- 3
|
||||
write$ -- 18
|
||||
(There was 1 warning)
|
||||
102
temp/presentation.nav
Normal file
102
temp/presentation.nav
Normal file
@@ -0,0 +1,102 @@
|
||||
\headcommand {\slideentry {0}{0}{1}{1/1}{}{0}}
|
||||
\headcommand {\beamer@framepages {1}{1}}
|
||||
\headcommand {\beamer@sectionpages {1}{1}}
|
||||
\headcommand {\beamer@subsectionpages {1}{1}}
|
||||
\headcommand {\sectionentry {1}{Introduction}{2}{Introduction}{0}}
|
||||
\headcommand {\beamer@subsectionpages {2}{1}}
|
||||
\headcommand {\beamer@subsectionentry {0}{1}{1}{2}{Motivation}}
|
||||
\headcommand {\slideentry {1}{1}{1}{2/2}{Motivation}{0}}
|
||||
\headcommand {\beamer@framepages {2}{2}}
|
||||
\headcommand {\slideentry {1}{1}{2}{3/3}{Motivation}{0}}
|
||||
\headcommand {\beamer@framepages {3}{3}}
|
||||
\headcommand {\slideentry {1}{1}{3}{4/4}{Motivation}{0}}
|
||||
\headcommand {\beamer@framepages {4}{4}}
|
||||
\headcommand {\beamer@subsectionpages {2}{4}}
|
||||
\headcommand {\beamer@subsectionentry {0}{1}{2}{5}{Context}}
|
||||
\headcommand {\slideentry {1}{2}{1}{5/6}{Context}{0}}
|
||||
\headcommand {\beamer@framepages {5}{6}}
|
||||
\headcommand {\beamer@sectionpages {2}{6}}
|
||||
\headcommand {\beamer@subsectionpages {5}{6}}
|
||||
\headcommand {\sectionentry {2}{Trajectory Optimization Background}{7}{Trajectory Optimization Background}{0}}
|
||||
\headcommand {\beamer@subsectionpages {7}{6}}
|
||||
\headcommand {\beamer@subsectionentry {0}{2}{1}{7}{System Dynamics}}
|
||||
\headcommand {\slideentry {2}{1}{1}{7/7}{System Dynamics}{0}}
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
\headcommand {\beamer@sectionpages {7}{17}}
|
||||
\headcommand {\beamer@subsectionpages {16}{17}}
|
||||
\headcommand {\sectionentry {3}{Algorithm Overview}{18}{Algorithm Overview}{0}}
|
||||
\headcommand {\beamer@subsectionpages {18}{17}}
|
||||
\headcommand {\beamer@subsectionentry {0}{3}{1}{18}{Trajectory Composition}}
|
||||
\headcommand {\slideentry {3}{1}{1}{18/22}{Trajectory Composition}{0}}
|
||||
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|
||||
\headcommand {\beamer@subsectionpages {18}{22}}
|
||||
\headcommand {\beamer@subsectionentry {0}{3}{2}{23}{Inner Loop Implementation}}
|
||||
\headcommand {\slideentry {3}{2}{1}{23/23}{Inner Loop Implementation}{0}}
|
||||
\headcommand {\beamer@framepages {23}{23}}
|
||||
\headcommand {\slideentry {3}{2}{2}{24/24}{Inner Loop Implementation}{0}}
|
||||
\headcommand {\beamer@framepages {24}{24}}
|
||||
\headcommand {\slideentry {3}{2}{3}{25/25}{Inner Loop Implementation}{0}}
|
||||
\headcommand {\beamer@framepages {25}{25}}
|
||||
\headcommand {\slideentry {3}{2}{4}{26/26}{Inner Loop Implementation}{0}}
|
||||
\headcommand {\beamer@framepages {26}{26}}
|
||||
\headcommand {\beamer@subsectionpages {23}{26}}
|
||||
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|
||||
\headcommand {\slideentry {3}{3}{1}{27/27}{Outer Loop Implementation}{0}}
|
||||
\headcommand {\beamer@framepages {27}{27}}
|
||||
\headcommand {\slideentry {3}{3}{2}{28/28}{Outer Loop Implementation}{0}}
|
||||
\headcommand {\beamer@framepages {28}{28}}
|
||||
\headcommand {\beamer@sectionpages {18}{28}}
|
||||
\headcommand {\beamer@subsectionpages {27}{28}}
|
||||
\headcommand {\sectionentry {4}{Sample Mission Analysis}{29}{Sample Mission Analysis}{0}}
|
||||
\headcommand {\beamer@subsectionpages {29}{28}}
|
||||
\headcommand {\beamer@subsectionentry {0}{4}{1}{29}{Mission Scenario}}
|
||||
\headcommand {\slideentry {4}{1}{1}{29/29}{Mission Scenario}{0}}
|
||||
\headcommand {\beamer@framepages {29}{29}}
|
||||
\headcommand {\slideentry {4}{1}{2}{30/30}{Mission Scenario}{0}}
|
||||
\headcommand {\beamer@framepages {30}{30}}
|
||||
\headcommand {\beamer@subsectionpages {29}{30}}
|
||||
\headcommand {\beamer@subsectionentry {0}{4}{2}{31}{Trajectory 1}}
|
||||
\headcommand {\slideentry {4}{2}{1}{31/34}{Trajectory 1}{0}}
|
||||
\headcommand {\beamer@framepages {31}{34}}
|
||||
\headcommand {\beamer@subsectionpages {31}{34}}
|
||||
\headcommand {\beamer@subsectionentry {0}{4}{3}{35}{Trajectory 2}}
|
||||
\headcommand {\slideentry {4}{3}{1}{35/38}{Trajectory 2}{0}}
|
||||
\headcommand {\beamer@framepages {35}{38}}
|
||||
\headcommand {\beamer@subsectionpages {35}{38}}
|
||||
\headcommand {\beamer@subsectionentry {0}{4}{4}{39}{Results Analysis}}
|
||||
\headcommand {\slideentry {4}{4}{1}{39/39}{Results Analysis}{0}}
|
||||
\headcommand {\beamer@framepages {39}{39}}
|
||||
\headcommand {\beamer@sectionpages {29}{39}}
|
||||
\headcommand {\beamer@subsectionpages {39}{39}}
|
||||
\headcommand {\sectionentry {5}{Conclusion}{40}{Conclusion}{0}}
|
||||
\headcommand {\slideentry {5}{0}{1}{40/40}{}{0}}
|
||||
\headcommand {\beamer@framepages {40}{40}}
|
||||
\headcommand {\beamer@partpages {1}{41}}
|
||||
\headcommand {\beamer@subsectionpages {40}{41}}
|
||||
\headcommand {\beamer@sectionpages {40}{41}}
|
||||
\headcommand {\beamer@documentpages {41}}
|
||||
\headcommand {\gdef \inserttotalframenumber {29}}
|
||||
17
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||||
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||||
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temp/presentation.snm
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temp/presentation.snm
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198
temp/thesis.bbl
Normal file
198
temp/thesis.bbl
Normal file
@@ -0,0 +1,198 @@
|
||||
\begin{thebibliography}{10}
|
||||
|
||||
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|
||||
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||||
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|
||||
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|
||||
|
||||
\bibitem{battin1984elegant}
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
|
||||
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||||
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||||
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||||
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||||
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||||
|
||||
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|
||||
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|
||||
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|
||||
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||||
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||||
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||||
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||||
|
||||
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||||
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|
||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
\bibitem{wachter2006implementation}
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||||
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||||
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||||
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||||
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|
||||
|
||||
\bibitem{wales1997global}
|
||||
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|
||||
\newblock Global optimization by basin-hopping and the lowest energy structures
|
||||
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|
||||
\newblock {\em The Journal of Physical Chemistry A}, 101(28):5111--5116, 1997.
|
||||
|
||||
\bibitem{wie1998space}
|
||||
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|
||||
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|
||||
\newblock Aiaa, 1998.
|
||||
|
||||
\end{thebibliography}
|
||||
62
temp/thesis.blg
Normal file
62
temp/thesis.blg
Normal file
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|
||||
This is BibTeX, Version 0.99d (TeX Live 2021/Arch Linux)
|
||||
Capacity: max_strings=200000, hash_size=200000, hash_prime=170003
|
||||
The top-level auxiliary file: temp//thesis.aux
|
||||
The style file: plain.bst
|
||||
Database file #1: LaTeX/thesis.bib
|
||||
Warning--entry type for "snow" isn't style-file defined
|
||||
--line 12 of file LaTeX/thesis.bib
|
||||
Warning--empty institution in blanchard1969unified
|
||||
Warning--empty booktitle in Casalino2007IndirectOM
|
||||
Warning--empty journal in cybulski1965results
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
Warning--empty journal in sims1999preliminary
|
||||
Warning--empty journal in stough2021nasa
|
||||
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|
||||
You've used 34 entries,
|
||||
2118 wiz_defined-function locations,
|
||||
690 strings with 9651 characters,
|
||||
and the built_in function-call counts, 10595 in all, are:
|
||||
= -- 992
|
||||
> -- 567
|
||||
< -- 5
|
||||
+ -- 230
|
||||
- -- 190
|
||||
* -- 743
|
||||
:= -- 1825
|
||||
add.period$ -- 100
|
||||
call.type$ -- 34
|
||||
change.case$ -- 192
|
||||
chr.to.int$ -- 0
|
||||
cite$ -- 47
|
||||
duplicate$ -- 386
|
||||
empty$ -- 800
|
||||
format.name$ -- 190
|
||||
if$ -- 2143
|
||||
int.to.chr$ -- 0
|
||||
int.to.str$ -- 34
|
||||
missing$ -- 37
|
||||
newline$ -- 170
|
||||
num.names$ -- 68
|
||||
pop$ -- 231
|
||||
preamble$ -- 1
|
||||
purify$ -- 163
|
||||
quote$ -- 0
|
||||
skip$ -- 259
|
||||
stack$ -- 0
|
||||
substring$ -- 522
|
||||
swap$ -- 48
|
||||
text.length$ -- 5
|
||||
text.prefix$ -- 0
|
||||
top$ -- 0
|
||||
type$ -- 122
|
||||
warning$ -- 13
|
||||
while$ -- 96
|
||||
width$ -- 36
|
||||
write$ -- 346
|
||||
(There were 14 warnings)
|
||||
41
temp/thesis.out
Normal file
41
temp/thesis.out
Normal file
@@ -0,0 +1,41 @@
|
||||
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|
||||
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|
||||
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||||
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|
||||
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|
||||
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||||
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||||
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||||
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||||
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||||
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||||
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|
||||
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||||
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||||
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||||
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||||
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|
||||
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||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
\BOOKMARK [2][-]{subsection.5.1.2}{\376\377\000F\000l\000y\000b\000y\000s\000\040\000A\000n\000a\000l\000y\000z\000e\000d}{section.5.1}% 36
|
||||
\BOOKMARK [1][-]{section.5.2}{\376\377\000F\000a\000s\000t\000e\000r\000,\000\040\000L\000e\000s\000s\000\040\000E\000f\000f\000i\000c\000i\000e\000n\000t\000\040\000T\000r\000a\000j\000e\000c\000t\000o\000r\000y}{chapter.5}% 37
|
||||
\BOOKMARK [1][-]{section.5.3}{\376\377\000S\000l\000o\000w\000e\000r\000,\000\040\000M\000o\000r\000e\000\040\000E\000f\000f\000i\000c\000i\000e\000n\000t\000\040\000T\000r\000a\000j\000e\000c\000t\000o\000r\000y}{chapter.5}% 38
|
||||
\BOOKMARK [1][-]{section.5.4}{\376\377\000F\000i\000n\000a\000l\000\040\000T\000r\000a\000j\000e\000c\000t\000o\000r\000y\000\040\000A\000n\000a\000l\000y\000s\000i\000s}{chapter.5}% 39
|
||||
\BOOKMARK [0][-]{chapter.6}{\376\377\000C\000o\000n\000c\000l\000u\000s\000i\000o\000n}{}% 40
|
||||
\BOOKMARK [-1][-]{chapter*.5}{\376\377\000\040\000B\000i\000b\000l\000i\000o\000g\000r\000a\000p\000h\000y}{}% 41
|
||||
Reference in New Issue
Block a user