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Unless Bosanac has a last minute change, the paper is done!

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Connor
2022-03-15 20:34:31 -06:00
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LaTeX/approach.tex
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@@ -264,7 +264,7 @@
\item The $v_{\infty,in}$ vector representing excess velocity at the
planetary flyby (or completion of mission) at the end of the phase
\item The time of flight for the phase
\item The unit-thrust profile in a sun-fixed frame represented by a
\item The unit-thrust profile in a sun-centered frame represented by a
series of vectors with each element ranging from 0 to 1.
\end{itemize}
\end{itemize}
@@ -397,18 +397,12 @@
non-powered flyby.
From these two velocity vectors the turning angle, and thus the periapsis of the flyby,
can then be calculated by Equation~\ref{turning_angle_eq} and the following equation:
\begin{equation}
r_p = \frac{\mu}{\vec{v}_{\infty,in} \cdot \vec{v}_{\infty,out}} \cdot \left(
\frac{1}{\sin(\delta/2)} - 1 \right)
\end{equation}
If this radius of periapse is then found to be less than the minimum safe radius
(currently set to the radius of the planet plus 100 kilometers), then the process is
repeated with new random flyby velocities until a valid seed flyby is found. These
checks are also performed each time a mission is perturbed or generated by the NLP
solver.
can then be calculated by Equation~\ref{turning_angle_eq} and
Equation~\ref{periapsis_eq}. If this radius of periapse is then found to be less than
the minimum safe radius (currently set to the radius of the planet plus 100 kilometers),
then the process is repeated with new random flyby velocities until a valid seed flyby
is found. These checks are also performed each time a mission is perturbed or generated
by the NLP solver.
The final requirement then, is the thrust controls, which are actually quite simple.
Since the thrust is defined as a 3-vector of values between -1 and 1 representing some