https://en.formulasearchengine.com/w/api.php?action=feedcontributions&feedformat=atom&user=24.205.0.0%2F16formulasearchengine - User contributions [en]2026-09-20T01:36:47ZUser contributionsMediaWiki 1.47.0-wmf.7https://en.formulasearchengine.com/w/index.php?title=Friedmann_equations&diff=7702Friedmann equations2014-01-28T16:30:28Z<p>24.205.239.229: Clarify: the term 'critical density' was used before it was defined</p>
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<div>In [[statics]], '''Lami's theorem''' is an equation relating the magnitudes of three [[coplanar]], [[Concurrent lines|concurrent]] and [[Coplanarity|non-collinear]] forces, which keeps an object in [[static equilibrium]], with the angles directly opposite to the corresponding forces. A,B,C<br />
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:where ''A'', ''B'' and ''C'' are the magnitudes of three coplanar, concurrent and non-collinear forces, which keep the object in static equilibrium, and<br />
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:''&alpha;'', ''&beta;'' and ''&gamma;'' are the angles directly opposite to the forces ''A'', ''B'' and ''C'' respectively.<br />
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:<math>\Rightarrow \frac{A}{\sin \alpha}=\frac{B}{\sin \beta}=\frac{C}{\sin \gamma}</math><br />
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:[[File:Lami.png|alt=Lami's Theorem]]<br />
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Lami's theorem is applied in static analysis of mechanical and structural systems. The theorem is named after [[Bernard Lamy (mathematician)|Bernard Lamy]].<br />
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==Proof of Lami's Theorem==<br />
Suppose there are three coplanar, concurrent and non-collinear forces, which keeps the object in static equilibrium. By the [[Euclidean vector|triangle law]], we can re-construct the diagram as follow:<br />
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:[[File:LamiProof.png]]<br />
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By the [[law of sines]],<br />
:<math>\frac{A}{\sin (\pi - \alpha)}=\frac{B}{\sin (\pi - \beta)}=\frac{C}{\sin (\pi - \gamma)}</math><br />
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:<math>\Rightarrow \frac{A}{\sin \alpha}=\frac{B}{\sin \beta}=\frac{C}{\sin \gamma}</math><br />
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==See also==<br />
* [[Law of sines]]<br />
* [[Mechanical equilibrium]]<br />
* [[Bernard Lamy (mathematician)]]<br />
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==Further reading==<br />
* R.K. Bansal (2005). "A Textbook of Engineering Mechanics". Laxmi Publications. p. 4. ISBN 978-81-7008-305-4.<br />
* I.S. Gujral (2008). "Engineering Mechanics". Firewall Media. p. 10. ISBN 978-81-318-0295-3<br />
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[[Category:Statics]]<br />
[[Category:Physics theorems]]</div>24.205.239.229https://en.formulasearchengine.com/w/index.php?title=Sedimentation_potential&diff=256005Sedimentation potential2012-06-07T17:45:42Z<p>24.205.233.186: /* Related Topics */</p>
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