From 38feb9b1c5d1ac978b02f215108c9870aa57373b Mon Sep 17 00:00:00 2001
From: Marcello Seri <marcello.seri@gmail.com>
Date: Tue, 23 Jul 2024 10:45:57 +0200
Subject: [PATCH] Update

Signed-off-by: Marcello Seri <marcello.seri@gmail.com>
---
 hm.tex                               |    5 +-
 images/potential-curves-pendulum.pdf |  Bin 49030 -> 34703 bytes
 images/potential-curves-pendulum.svg | 1126 +++++++++++++++++++-------
 3 files changed, 818 insertions(+), 313 deletions(-)

diff --git a/hm.tex b/hm.tex
index 7ee11a1..50baf5c 100644
--- a/hm.tex
+++ b/hm.tex
@@ -871,15 +871,14 @@ \chapter*{Preface}
         \item In the case of the spring, also called the \emph{harmonic oscillator}, $U(x) = \frac12 \omega^2 x^2$ and the integral curves are of the form $y^2 + \omega^2 x^2 = C$.
           Recalling \eqref{eq:springsol}, $C = \omega^2 R^2 \geq 0$ and the curves are ellipses parametrized by $C$.
           This will be a very important example throughout the course.
+          \warpHTMLonly{<div align=center><iframe height=490 width=800 src=https://editor.p5js.org/mseri/full/kU1aO7EoZ style=border:none;></iframe><p>Use the sliders to see how the phase plane is changing. What happens if you vary the mass?</p></div>}
         \item In the case of the pendulum, $U(x) = -\omega^2 \cos(x)$ and the integral curves are solutions of $\frac12 y^2 - \omega^2 \cos(x) = C$, $C \geq -\omega^2$.
           Even though we cannot easily give a time parametrization of the motion itself, this formalism allows us to immediately describe the evolution of the system.
           We will come back to this fact in more generality in the next section.
+          \warpHTMLonly{<div align=center><iframe height=515 width=800 src=https://editor.p5js.org/mseri/full/iar8GHKTU style=border:none;></iframe><p>Use the sliders to see how the phase plane is changing. What happens if you vary the mass?</p></div>}
       \end{itemize}
     \end{example}
 
-    \warpHTMLonly{<div align=center><iframe height=530 width=800 src=https://editor.p5js.org/mseri/full/iar8GHKTU></iframe></div>}
-    \warpHTMLonly{<div align=center><iframe height=530 width=800 src=https://editor.p5js.org/mseri/full/kU1aO7EoZ></iframe></div>}
-
     From these examples we already see that phase curves can consist of only one point. In such cases, the points are called \emph{equilibrium} points.
 
     \subsection{The conservation of energy}\label{sec:energy}
diff --git a/images/potential-curves-pendulum.pdf b/images/potential-curves-pendulum.pdf
index 9d0945493453acb5313fae02f5f32ec3eeefde75..94b499b8dd1336b6323431d052118ebe4470a042 100644
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