From b0ac372228452c906b0a53da0b0796548585a69a Mon Sep 17 00:00:00 2001
From: youainti <youainti@protonmail.com>
Date: Thu, 15 Jul 2021 16:42:31 -0700
Subject: [PATCH] just checking in what I have so far in order to merge.

---
 CurrentWriting/sections/01_LawsOfMotion.tex     |  8 ++++----
 CurrentWriting/sections/03_SurvivalAnalysis.tex | 10 +++++++---
 2 files changed, 11 insertions(+), 7 deletions(-)

diff --git a/CurrentWriting/sections/01_LawsOfMotion.tex b/CurrentWriting/sections/01_LawsOfMotion.tex
index 4465842..1c2efbb 100644
--- a/CurrentWriting/sections/01_LawsOfMotion.tex
+++ b/CurrentWriting/sections/01_LawsOfMotion.tex
@@ -50,9 +50,9 @@ Debris is generated by various processes, including:
 \begin{itemize}
     \item Naturally occuring debris
     \item Satellite launches, operations, failures, or intentional destruction.
-    \item Collisions between satellites
-    \item Collisions between satellites and debris
-    \item Collisions between debris
+    \item Collisions between two satellites
+    \item Collisions between a satellite and debris
+    \item Collisions between pieces of debris
 \end{itemize}
 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}
     D_{t+1} = (1-\delta)D_t + g(D_t) + \gamma(\{s^j_t\},D_t) + \Gamma(\{x^j_t\})
 \end{align}
-I formulate this more specifically as:
+For simplicity, I formulate this more specifically as:
 \begin{align}
     D_{t+1} = (1-\delta)D_t + g(D_t) 
                 + \sum^N_{i=1} \gamma l^i(\{s^j_t\},D_t)
diff --git a/CurrentWriting/sections/03_SurvivalAnalysis.tex b/CurrentWriting/sections/03_SurvivalAnalysis.tex
index 20d264b..fc68a63 100644
--- a/CurrentWriting/sections/03_SurvivalAnalysis.tex
+++ b/CurrentWriting/sections/03_SurvivalAnalysis.tex
@@ -2,15 +2,19 @@
 \graphicspath{{\subfix{Assets/img/}}}
 
 \begin{document}
-In his dissertation \cite{RaoDissertation} briefly examines the "survival rates" of a satellite constellation.
-I've applied this to my model and extended the results.
+In his dissertation \cite{RaoDissertation} briefly examines the ''survival rates" of 
+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, 
 %i.e. an elasticity of risk.
 
 %I should probably look up how to analyze changes in risk level and quantitative representations etc.
 
 % 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 $t+1$.
 Thus the marginal survival rate represents the additional loss of
 satellites due to a slightly larger constellation or fleet stock.