just checking in what I have so far in order to merge.

temporaryWork
youainti 5 years ago
parent cc5466d7b0
commit b0ac372228

@ -50,9 +50,9 @@ Debris is generated by various processes, including:
\begin{itemize} \begin{itemize}
\item Naturally occuring debris \item Naturally occuring debris
\item Satellite launches, operations, failures, or intentional destruction. \item Satellite launches, operations, failures, or intentional destruction.
\item Collisions between satellites \item Collisions between two satellites
\item Collisions between satellites and debris \item Collisions between a satellite and debris
\item Collisions between debris \item Collisions between pieces of debris
\end{itemize} \end{itemize}
Debris leaves orbit when atmospheric drag slows it down enough to reenter the atmosphere. Debris leaves orbit when atmospheric drag slows it down enough to reenter the atmosphere.
@ -60,7 +60,7 @@ These effects can be represented by the following general law of motion.
\begin{align} \begin{align}
D_{t+1} = (1-\delta)D_t + g(D_t) + \gamma(\{s^j_t\},D_t) + \Gamma(\{x^j_t\}) D_{t+1} = (1-\delta)D_t + g(D_t) + \gamma(\{s^j_t\},D_t) + \Gamma(\{x^j_t\})
\end{align} \end{align}
I formulate this more specifically as: For simplicity, I formulate this more specifically as:
\begin{align} \begin{align}
D_{t+1} = (1-\delta)D_t + g(D_t) D_{t+1} = (1-\delta)D_t + g(D_t)
+ \sum^N_{i=1} \gamma l^i(\{s^j_t\},D_t) + \sum^N_{i=1} \gamma l^i(\{s^j_t\},D_t)

@ -2,15 +2,19 @@
\graphicspath{{\subfix{Assets/img/}}} \graphicspath{{\subfix{Assets/img/}}}
\begin{document} \begin{document}
In his dissertation \cite{RaoDissertation} briefly examines the "survival rates" of a satellite constellation. In his dissertation \cite{RaoDissertation} briefly examines the ''survival rates" of
I've applied this to my model and extended the results. a satellite constellation.
Applying the same analysis to this formulation of the law of motion
for satellite stocks (\cref{Add in}) clarifies some details on risk burdens
with highly asymmectical conditions.
%This approach allows us to construct a elasticity of survival and satellite additions, %This approach allows us to construct a elasticity of survival and satellite additions,
%i.e. an elasticity of risk. %i.e. an elasticity of risk.
%I should probably look up how to analyze changes in risk level and quantitative representations etc. %I should probably look up how to analyze changes in risk level and quantitative representations etc.
% Marginal survival. % Marginal survival.
The survival rate for a constellation $i$ is defined as $R^i = 1-l^i(\cdot)$, i.e. the proportion of satellites- The survival rate for a constellation $i$ is defined as $R^i = 1-l^i(\cdot)$,
i.e. the proportion of satellites
that were not lost (degraded nor destroyed) between period $t$ and $t+1$. that were not lost (degraded nor destroyed) between period $t$ and $t+1$.
Thus the marginal survival rate represents the additional loss of Thus the marginal survival rate represents the additional loss of
satellites due to a slightly larger constellation or fleet stock. satellites due to a slightly larger constellation or fleet stock.

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