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<!DOCTYPE html>
<html>
<head>
<title>Ch. $CHAPTER-NUM$ - $CHAPTER-NAME$</title>
<meta name="Ch. $CHAPTER-NUM$ - $CHAPTER-NAME$" content="text/html; charset=utf-8;" />
<link rel="canonical" href="http://underactuated.mit.edu/$CHAPTER-ID$.html" />
<script src="https://hypothes.is/embed.js" async></script>
<script type="text/javascript" src="chapters.js"></script>
<script type="text/javascript" src="htmlbook/book.js"></script>
<script src="htmlbook/mathjax-config.js" defer></script>
<script type="text/javascript" id="MathJax-script" defer
src="htmlbook/MathJax/es5/tex-chtml.js">
</script>
<script>window.MathJax || document.write('<script type="text/javascript" src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-chtml.js" defer><\/script>')</script>
<link rel="stylesheet" href="htmlbook/highlight/styles/default.css">
<script src="htmlbook/highlight/highlight.pack.js"></script> <!-- http://highlightjs.readthedocs.io/en/latest/css-classes-reference.html#language-names-and-aliases -->
<script>hljs.initHighlightingOnLoad();</script>
<link rel="stylesheet" type="text/css" href="htmlbook/book.css" />
</head>
<body onload="loadChapter('underactuated');">
<div data-type="titlepage">
<header>
<h1><a href="index.html" style="text-decoration:none;">Underactuated Robotics</a></h1>
<p data-type="subtitle">Algorithms for Walking, Running, Swimming, Flying, and Manipulation</p>
<p style="font-size: 18px;"><a href="http://people.csail.mit.edu/russt/">Russ Tedrake</a></p>
<p style="font-size: 14px; text-align: right;">
© Russ Tedrake, 2023<br/>
Last modified <span id="last_modified"></span>.</br>
<script>
var d = new Date(document.lastModified);
document.getElementById("last_modified").innerHTML = d.getFullYear() + "-" + (d.getMonth()+1) + "-" + d.getDate();</script>
<a href="misc.html">How to cite these notes, use annotations, and give feedback.</a><br/>
</p>
</header>
</div>
<p><b>Note:</b> These are working notes used for <a
href="https://underactuated.csail.mit.edu/Spring2023/">a course being taught
at MIT</a>. They will be updated throughout the Spring 2023 semester. <a
href="https://www.youtube.com/channel/UChfUOAhz7ynELF-s_1LPpWg">Lecture videos are available on YouTube</a>.</p>
<table style="width:100%;"><tr style="width:100%">
<td style="width:33%;text-align:left;"><a class="previous_chapter"></a></td>
<td style="width:33%;text-align:center;"><a href=index.html>Table of contents</a></td>
<td style="width:33%;text-align:right;"><a class="next_chapter"></a></td>
</tr></table>
<script type="text/javascript">document.write(notebook_header('$CHAPTER-ID$'))
</script>
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