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Update manuscript to satisfy JGCD
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skulumani committed Mar 9, 2019
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18 changes: 9 additions & 9 deletions manuscript.tex
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Expand Up @@ -94,10 +94,10 @@ \section{Introduction}
The coupling is induced due to the different gravitational forces experienced on various portions of the spacecraft.
The effect of the gravitational coupling is related to the ratio of the spacecraft size and orbital radius~\cite{hughes2004}.
For operations around asteroids, the ratio is relatively large which causes a much larger coupling between the translational and rotational states.
References~\citenum{elmasri2005} and~\citenum{sanyal2004a} investigated the coupling of an elastic dumbbell spacecraft in orbit about a central body, but only considered the case of a spherically symmetric central body.
\citeauthor{elmasri2005}~\cite{elmasri2005} and \citeauthor{sanyal2004a}~\cite{sanyal2004a} investigated the coupling of an elastic dumbbell spacecraft in orbit about a central body, but only considered the case of a spherically symmetric central body.
Furthermore, the spacecraft model is assumed to remain in a planar orbit.
As a result, these developments are not directly applicable to motion about an asteroid, which experiences highly non-Keplerian motion.
Reference~\citenum{misra2015b} investigated the effect of coupled motion on long term trajectories around asteroids.
\citeauthor{misra2015b}~\cite{misra2015b} investigated the effect of coupled motion on long term trajectories around asteroids.
However, the analysis only considered a second order spherical harmonic gravitational potential model.
Therefore, these results are only valid when far from the asteroid surface and will diverge when used within the Brillouin sphere.

Expand Down Expand Up @@ -825,8 +825,8 @@ \subsection{Numerical Example}
Areas which violate the slope constraint of \( \phi < \SI{5}{\degree} \) are excluded from further consideration.
\begin{figure}[htbp]
\centering
\subcaptionbox{Surface slope of Castalia\label{fig:surface_slope_castalia}}{\includegraphics[width=0.5\textwidth]{dynamic_exploration_castalia_refine_slope.pdf}}%
\subcaptionbox{Masked surface slope with areas \( \phi > \SI{5}{\degree}\) excluded\label{fig:surface_slope_castalia_masked}}{\includegraphics[width=0.5\textwidth,keepaspectratio]{dynamic_exploration_castalia_refine_slope_masked.pdf}}
\subcaptionbox{Surface slope of Castalia\label{fig:surface_slope_castalia}}{\includegraphics[width=\textwidth]{dynamic_exploration_castalia_refine_slope.pdf}}\\
\subcaptionbox{Masked surface slope with areas \( \phi > \SI{5}{\degree}\) excluded\label{fig:surface_slope_castalia_masked}}{\includegraphics[width=\textwidth,keepaspectratio]{dynamic_exploration_castalia_refine_slope_masked.pdf}}
\caption{Surface slope of asteroid Castalia\label{fig:surface_slope_castalia_both}}
\end{figure}

Expand All @@ -837,15 +837,15 @@ \subsection{Numerical Example}
The area immediately beneath the spacecraft has a small cost while those on the opposite side of the asteroid have a much larger cost.
\begin{figure}[htbp]
\centering
\subcaptionbox{Surface Distance to surface of Castalia\label{fig:surface_distance_castalia}}{\includegraphics[width=0.5\textwidth]{dynamic_exploration_castalia_refine_dist.pdf}}%
\subcaptionbox{Masked distance to surface with areas \( \phi > \SI{5}{\degree}\) excluded\label{fig:surface_distance_castalia_masked}}{\includegraphics[width=0.5\textwidth,keepaspectratio]{dynamic_exploration_castalia_refine_dist_masked.pdf}}
\subcaptionbox{Surface Distance to surface of Castalia\label{fig:surface_distance_castalia}}{\includegraphics[width=\textwidth]{dynamic_exploration_castalia_refine_dist.pdf}}\\
\subcaptionbox{Masked distance to surface with areas \( \phi > \SI{5}{\degree}\) excluded\label{fig:surface_distance_castalia_masked}}{\includegraphics[width=\textwidth,keepaspectratio]{dynamic_exploration_castalia_refine_dist_masked.pdf}}
\caption{Distance to surface of asteroid Castalia\label{fig:distance_castalia_both}}
\end{figure}
We can combine~\cref{fig:distance_castalia_both,fig:surface_slope_castalia_both} to determine the best landing site.
The combination of the two is shown in~\cref{fig:landing_site_cost} with the desired landing site shown by the blue marker.
\begin{figure}[htbp]
\centering
\includegraphics[width=0.75\textwidth,keepaspectratio]{dynamic_exploration_castalia_refine_cost.pdf}
\includegraphics[width=\textwidth,keepaspectratio]{dynamic_exploration_castalia_refine_cost.pdf}
\caption{Total cost for surface landing based on surface slope and distance\label{fig:landing_site_cost}}
\end{figure}
After selecting the appropriate landing site we then prepare for landing by collecting more measurements in the region around the landing area.
Expand All @@ -870,8 +870,8 @@ \subsection{Numerical Example}
\Cref{fig:castalia_refine_density} shows that the vertex density increases by approximately an order of magnitude in region immediately surround the landing site.
\begin{figure}[htbp]
\centering
\subcaptionbox{Original vertex density of the initial shape estimate\label{fig:intial_vertex_density}}{\includegraphics[width=0.5\textwidth]{dynamic_exploration_castalia_refine_density.pdf}}%
\subcaptionbox{Vertex density after refinement around landing site\label{fig:refine_vertex_density}}{\includegraphics[width=0.5\textwidth]{dynamic_exploration_castalia_land_density.pdf}}
\subcaptionbox{Original vertex density of the initial shape estimate\label{fig:intial_vertex_density}}{\includegraphics[width=\textwidth]{dynamic_exploration_castalia_refine_density.pdf}}\\
\subcaptionbox{Vertex density after refinement around landing site\label{fig:refine_vertex_density}}{\includegraphics[width=\textwidth]{dynamic_exploration_castalia_land_density.pdf}}
\caption{Vertex density before and after refinement at asteroid Castalia\label{fig:castalia_refine_density}}
\end{figure}

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