She did. Now I'm done!

LaTeX/introduction.tex

@@ -1,16 +1,16 @@
 \chapter{Introduction}
 
 	Continuous low-thrust engines utilizing technologies such as Ion propulsion, Hall thrusters, and
-	others can be a powerful system in the enabling of long-range interplanetary missions with fuel
-	efficiencies unrivaled by those that employ only impulsive thrust systems. The challenge in
-	utilizing these systems, then, is the design of trajectories that effectively utilize this
-	technology. Continuous thrust propulsive systems tend to be particularly suited to missions
-	which require very high total change in velocity ($\Delta V$) values and take place over a
-	particularly long duration. Traditional impulsive thrusting techniques can achieve these changes
-	in velocity, but typically have a far lower specific impulse and, as such, are much less fuel
-	efficient, costing the mission valuable financial resources that could instead be used for
-	science. Because of their inherently high specific impulse (and thus efficiency), low-thrust
-	propagation systems are well-suited to interplanetary missions.
+	others enable long-range interplanetary missions with fuel efficiencies unrivaled by those that
+	employ only impulsive thrust systems. The challenge in utilizing these systems, then, is the
+	design of trajectories that effectively utilize this technology. Continuous thrust propulsive
+	systems tend to be particularly suited to missions which require very high total change in
+	velocity ($\Delta V$) values and take place over a particularly long duration. Traditional
+	impulsive thrusting techniques can achieve these changes in velocity, but typically have a far
+	lower specific impulse and, as such, are much less fuel efficient, costing the mission valuable
+	financial resources that could instead be used for science. Because of their inherently high
+	specific impulse (and thus efficiency), low-thrust propulsion systems are well-suited to
+	interplanetary missions.
 
 	The first attempt by NASA to use an electric ion-thruster for an interplanetary mission was the
 	Deep Space 1 mission\cite{brophy2002}. This mission was designed to test the ``new'' technology,
@@ -29,16 +29,15 @@
 	in October 2018 and is projected to perform a flyby of Earth, two of Venus, and six of
 	Mercury before inserting into an orbit around that planet.
 
-	A common theme in mission design is that there always exists a trade-off between efficiency
-	(particularly in terms of fuel use) and the time required to achieve the mission objective. Low
-	thrust systems in particular tend to produce mission profiles that sacrifice the rate of
-	convergence on the target state in order to achieve large increases in fuel efficiency. Often a
-	low-thrust mission profile in Earth orbit will require multiple orbital periods to achieve the
-	desired change in spacecraft state. Interplanetary missions, though, provide a particularly
-	useful case for continuous thrust technology. The trajectory arcs in interplanetary space are
-	generally much, much longer than orbital missions around the Earth. Because of this increase,
-	even a small continuous thrust is capable of producing large $\Delta V$ values over the course
-	of a single trajectory arc.
+	A common theme in mission design is that there is a trade-off between efficiency (particularly
+	in terms of fuel use) and the time required to achieve the mission objective. Low thrust systems
+	in particular tend to produce mission profiles that sacrifice the rate of convergence on the
+	target state in order to achieve large increases in fuel efficiency. Often a low-thrust transfer
+	in Earth orbit will require multiple orbital periods to achieve the desired change in spacecraft
+	state. Interplanetary missions, though, provide a particularly useful case for continuous thrust
+	technology. The trajectory arcs in interplanetary space are generally much, much longer than
+	orbital missions around the Earth. Because of this increase, even a small continuous thrust is
+	capable of producing large $\Delta V$ values over the course of a single trajectory arc.
 
 	Another technique often leveraged by interplanetary trajectory designers is the gravity assist.
 	Gravity assists utilize the inertia of a large planetary body to ``slingshot'' a spacecraft,
@@ -58,24 +57,22 @@
 	routine for producing unconstrained, globally optimal trajectories for realistic interplanetary
 	mission development that utilizes both planetary flybys and efficient low-thrust electric
 	propulsion techniques. Similar studies have also been performed by a number of researchers
-	including a team from JPL\cite{sims2006} as well as a Spanish team\cite{morante}, among several
-	others.
+	including a team from JPL\cite{sims2006}, among several others\cite{morante}.
 
-	This thesis will attempt to develop an algorithm for the optimization of low-thrust enabled
-	trajectories for initial feasibility analysis in mission design. The algorithm will utilize
-	a non-linear programming solver to directly optimize a set of control thrusts for the
-	user-provided flyby planets, for any provided cost function. A monotonic basin hopping algorithm
-	(MBH) will then be employed to traverse the search space in an effort to find additional local
-	optima. This approach differs from the work produced earlier by Englander and the other teams,
-	but is largely meant to explore the feasibility of such techniques and propose a few
-	enhancements. The approach defined in this thesis will then be used to investigate an example
-	mission to Saturn.
+	This thesis focuses on optimization of low-thrust enabled trajectories that use gravity assists.
+	The approach uses a non-linear programming solver to directly optimize a set of control thrusts
+	for the user-provided flyby planets, for any provided cost function. A monotonic basin hopping
+	algorithm (MBH) is then employed to traverse the search space in an effort to find additional
+	local optima. This approach differs from the work produced earlier by Englander and the other
+	teams, but is largely meant to explore the feasibility of such techniques and propose a few
+	enhancements. The approach defined in this thesis is then used to design low thrust trajectories
+	with gravity assits from the Earth to Saturn.
 
-	This thesis will explore these concepts in a number of different sections. Section
-	\ref{traj_dyn} will explore the basic dynamical principles of trajectory design, beginning the
-	with fundamental system dynamics, then exploring interplanetary system dynamics and gravity
-	flybys, and finally the dynamics that are specific to low-thrust enabled trajectories. Section
-	\ref{traj_optimization} will then discuss process of optimizing spacecraft trajectories in
-	general and the tool available for that. Section \ref{algorithm} will cover the implementation
-	details of the optimization algorithm developed for this paper. Finally, section \ref{results}
-	will explore the results of some hypothetical missions to Saturn.
+	This thesis is organized as follows: Section \ref{traj_dyn} will explore the basic dynamical
+	principles of trajectory design, beginning the with fundamental system dynamics, then exploring
+	interplanetary system dynamics and gravity flybys, and finally the dynamics that are specific to
+	low-thrust enabled trajectories. Section \ref{traj_optimization} will then discuss process of
+	optimizing spacecraft trajectories in general and the tool available for that. Section
+	\ref{algorithm} will cover the implementation details of the optimization algorithm developed
+	for this paper. Finally, section \ref{results} will explore the results of some hypothetical
+	missions to Saturn.