From c7149a38c8479f93109063027fdc7cdbbcc1f095 Mon Sep 17 00:00:00 2001
From: Lorenzo Van Munoz <66997677+lord-zo@users.noreply.github.com>
Date: Tue, 9 Feb 2021 14:03:22 -0800
Subject: [PATCH] Fix Hamilton's equations

---
 knitr/planetary_motion/planetary_motion.rmd | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/knitr/planetary_motion/planetary_motion.rmd b/knitr/planetary_motion/planetary_motion.rmd
index e6110edec..28487049c 100644
--- a/knitr/planetary_motion/planetary_motion.rmd
+++ b/knitr/planetary_motion/planetary_motion.rmd
@@ -83,7 +83,7 @@ The motion of the planet is described by Newton's law of motion, which is a seco
 For convenience, we use Hamilton's formulation of the law, which is based on a system of two first-order differential equations,
 \begin{eqnarray*}
   \frac{\mathrm d q}{\mathrm d t} & = & \frac{p}{m}, \\
-  \frac{\mathrm d q}{\mathrm d t} & = & - \frac{k}{r^3} (q - q_*),
+  \frac{\mathrm d p}{\mathrm d t} & = & - \frac{k}{r^3} (q - q_*),
 \end{eqnarray*}
 where $k = GmM = 10^{-3}M$, and $r = \sqrt{(q - q_*)^T(q - q_*)}$ is the distance between the planet and the star.