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Notes for AKT-140115/0:30:33 - Revision history
2026-05-19T06:02:21Z
Revision history for this page on the wiki
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https://drorbn.net/index.php?title=Notes_for_AKT-140115/0:30:33&diff=16582&oldid=prev
Leo algknt at 06:22, 20 June 2018
2018-06-20T06:22:42Z
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<td style="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;"><br /></td>
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<td style="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;"><div>2. For a rigid body in <math>\mathbb{R}^3</math>, the configuration space is <math>\mathbb{R}^3 \times SO(3)</math>. Generally, it is <math>\mathbb{R}^n \times SO(n)</math>, where <math>SO(n)</math> is the special orthogonal group.</div></td>
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<td style="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;"><div>2. For a rigid body in <math>\mathbb{R}^3</math>, the configuration space is <math>\mathbb{R}^3 \times SO(3)</math>. Generally, it is <math>\mathbb{R}^n \times SO(n)</math>, where <math>SO(n)</math> is the special orthogonal group.</div></td>
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<td style="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;"><div>3. The torus with its diagonal removed is the configuration space of two points on <math>S^1</math>.</div></td>
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<td style="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;"><div>3. The torus with its diagonal removed<ins style="font-weight: bold; text-decoration: none;">, <math>S^1 \times \mathbb{R}</math>,</ins> is the configuration space of two points on <math>S^1</math>.<ins style="font-weight: bold; text-decoration: none;"> This is <math>C_2(S^1)</math></ins></div></td>
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Leo algknt
https://drorbn.net/index.php?title=Notes_for_AKT-140115/0:30:33&diff=16581&oldid=prev
Leo algknt at 06:18, 20 June 2018
2018-06-20T06:18:47Z
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<td style="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;"><br /></td>
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<td style="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;"><div>2. For a rigid body in <math>\mathbb{R}^3</math>, the configuration space is <math>\mathbb{R}^3 \times SO(3)</math>. Generally, it is <math>\mathbb{R}^n \times SO(n)</math>, where <math>SO(n)</math> is the special orthogonal group.</div></td>
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<td style="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;"><div>2. For a rigid body in <math>\mathbb{R}^3</math>, the configuration space is <math>\mathbb{R}^3 \times SO(3)</math>. Generally, it is <math>\mathbb{R}^n \times SO(n)</math>, where <math>SO(n)</math> is the special orthogonal group.</div></td>
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Leo algknt
https://drorbn.net/index.php?title=Notes_for_AKT-140115/0:30:33&diff=16580&oldid=prev
Leo algknt at 06:16, 20 June 2018
2018-06-20T06:16:31Z
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<td style="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;"><br /></td>
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<td style="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;"><div>2. For a rigid body in <math>\mathbb{R}^3</math>, the configuration space is <math>\mathbb{R}^3 \times SO(3)</math>. Generally, it is <math>\mathbb{R}^n \times SO(n)</math>, where <math>SO(n)</math> is the special orthogonal group.</div></td>
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<td style="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;"><div>2. For a rigid body in <math>\mathbb{R}^3</math>, the configuration space is <math>\mathbb{R}^3 \times SO(3)</math>. Generally, it is <math>\mathbb{R}^n \times SO(n)</math>, where <math>SO(n)</math> is the special orthogonal group.</div></td>
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Leo algknt
https://drorbn.net/index.php?title=Notes_for_AKT-140115/0:30:33&diff=16579&oldid=prev
Leo algknt: Created page with "'''Configuration space''' Given a topological space <math>X</math>, the <math>n</math>th ordered configuration space of <math>X</math> denoted by <math>\mathrm{Conf}_n(X)</ma..."
2018-06-20T06:15:08Z
<p>Created page with "'''Configuration space''' Given a topological space <math>X</math>, the <math>n</math>th ordered configuration space of <math>X</math> denoted by <math>\mathrm{Conf}_n(X)</ma..."</p>
<p><b>New page</b></p><div>'''Configuration space''' Given a topological space <math>X</math>, the <math>n</math>th ordered configuration space of <math>X</math> denoted by <math>\mathrm{Conf}_n(X)</math> is the set of <math>n</math>-tuples of pairwise distinct points in <math>X</math>, that is <math>\mathrm{Conf}_n(X):= \prod^n X \setminus \{(x_1, \ldots, x_n) : x_i = x_j \;\mathrm{for} \;i\ne j\}</math>.<br />
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In physics, parameters are used to define the configuration of a system and the vector space defined by these parameters is the configuration space of the system. It is used to describe the state of a whole system as a single point in a higher-dimensional space.<br />
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'''Examples of Configuration space'''<br />
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1. The configuration space of a particle in <math>\mathbb{R}^3</math> is <math>\mathbb{R}^3</math>. For <math>n</math> particles in <math>\mathbb{R}^3</math>, it is <math>\mathbb{R}^{3n}</math><br />
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2. For a rigid body in <math>\mathbb{R}^3</math>, the configuration space is <math>\mathbb{R}^3 \times SO(3)</math>. Generally, it is <math>\mathbb{R}^n \times SO(n)</math>, where <math>SO(n)</math> is the special orthogonal group.</div>
Leo algknt