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	<id>https://spacetimegeometricalgebra.org/wiki/index.php?action=history&amp;feed=atom&amp;title=Velocity</id>
	<title>Velocity - Revision history</title>
	<link rel="self" type="application/atom+xml" href="https://spacetimegeometricalgebra.org/wiki/index.php?action=history&amp;feed=atom&amp;title=Velocity"/>
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	<updated>2026-04-29T14:38:50Z</updated>
	<subtitle>Revision history for this page on the wiki</subtitle>
	<generator>MediaWiki 1.40.0</generator>
	<entry>
		<id>https://spacetimegeometricalgebra.org/wiki/index.php?title=Velocity&amp;diff=11&amp;oldid=prev</id>
		<title>Eric Lengyel at 01:24, 20 November 2024</title>
		<link rel="alternate" type="text/html" href="https://spacetimegeometricalgebra.org/wiki/index.php?title=Velocity&amp;diff=11&amp;oldid=prev"/>
		<updated>2024-11-20T01:24:58Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
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				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 01:24, 20 November 2024&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l3&quot;&gt;Line 3:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 3:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;:$$\mathbf u = \dfrac{d\mathbf r}{d\tau} = \gamma c\,\mathbf e_0 + \gamma \dot x\,\mathbf e_1 + \gamma \dot y\,\mathbf e_2 + \gamma \dot z\,\mathbf e_3$$ ,&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;:$$\mathbf u = \dfrac{d\mathbf r}{d\tau} = \gamma c\,\mathbf e_0 + \gamma \dot x\,\mathbf e_1 + \gamma \dot y\,\mathbf e_2 + \gamma \dot z\,\mathbf e_3$$ ,&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br/&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br/&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;where $$\mathbf r$$ is the body's [[position]] and $$\tau$$ is proper time.&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;where $$\mathbf r$$ is the body's [[position]] and $$\tau$$ is proper &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;time. The velocity $$\mathbf u$$ has units of length / &lt;/ins&gt;time.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br/&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br/&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;== See Also ==&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;== See Also ==&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Eric Lengyel</name></author>
	</entry>
	<entry>
		<id>https://spacetimegeometricalgebra.org/wiki/index.php?title=Velocity&amp;diff=10&amp;oldid=prev</id>
		<title>Eric Lengyel: Created page with &quot;The velocity $$\mathbf u$$ of a body in spacetime is given by  :$$\mathbf u = \dfrac{d\mathbf r}{d\tau} = \gamma c\,\mathbf e_0 + \gamma \dot x\,\mathbf e_1 + \gamma \dot y\,\mathbf e_2 + \gamma \dot z\,\mathbf e_3$$ ,  where $$\mathbf r$$ is the body's position and $$\tau$$ is proper time.  == See Also ==  * Position * Momentum&quot;</title>
		<link rel="alternate" type="text/html" href="https://spacetimegeometricalgebra.org/wiki/index.php?title=Velocity&amp;diff=10&amp;oldid=prev"/>
		<updated>2024-11-20T01:24:07Z</updated>

		<summary type="html">&lt;p&gt;Created page with &amp;quot;The velocity $$\mathbf u$$ of a body in spacetime is given by  :$$\mathbf u = \dfrac{d\mathbf r}{d\tau} = \gamma c\,\mathbf e_0 + \gamma \dot x\,\mathbf e_1 + \gamma \dot y\,\mathbf e_2 + \gamma \dot z\,\mathbf e_3$$ ,  where $$\mathbf r$$ is the body&amp;#039;s &lt;a href=&quot;/wiki/index.php?title=Position&quot; title=&quot;Position&quot;&gt;position&lt;/a&gt; and $$\tau$$ is proper time.  == See Also ==  * &lt;a href=&quot;/wiki/index.php?title=Position&quot; title=&quot;Position&quot;&gt;Position&lt;/a&gt; * &lt;a href=&quot;/wiki/index.php?title=Momentum&quot; title=&quot;Momentum&quot;&gt;Momentum&lt;/a&gt;&amp;quot;&lt;/p&gt;
&lt;p&gt;&lt;b&gt;New page&lt;/b&gt;&lt;/p&gt;&lt;div&gt;The velocity $$\mathbf u$$ of a body in spacetime is given by&lt;br /&gt;
&lt;br /&gt;
:$$\mathbf u = \dfrac{d\mathbf r}{d\tau} = \gamma c\,\mathbf e_0 + \gamma \dot x\,\mathbf e_1 + \gamma \dot y\,\mathbf e_2 + \gamma \dot z\,\mathbf e_3$$ ,&lt;br /&gt;
&lt;br /&gt;
where $$\mathbf r$$ is the body's [[position]] and $$\tau$$ is proper time.&lt;br /&gt;
&lt;br /&gt;
== See Also ==&lt;br /&gt;
&lt;br /&gt;
* [[Position]]&lt;br /&gt;
* [[Momentum]]&lt;/div&gt;</summary>
		<author><name>Eric Lengyel</name></author>
	</entry>
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