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| 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
| | 39 year old Secondary College Teacher Dino Gohr from Fenelon Falls, likes to spend some time origami, diet and actions. Has completed a great around the world journey that consisted of traveling to the Pontcysyllte Aqueduct and Canal. |
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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
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| :''α'', ''β'' and ''γ'' are the angles directly opposite to the forces ''A'', ''B'' and ''C'' respectively.
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| :<math>\Rightarrow \frac{A}{\sin \alpha}=\frac{B}{\sin \beta}=\frac{C}{\sin \gamma}</math>
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| :[[File:Lami.png|alt=Lami's Theorem]]
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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]].
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| ==Proof of Lami's Theorem==
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| 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:
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| :[[File:LamiProof.png]]
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| By the [[law of sines]],
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| :<math>\frac{A}{\sin (\pi - \alpha)}=\frac{B}{\sin (\pi - \beta)}=\frac{C}{\sin (\pi - \gamma)}</math>
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| :<math>\Rightarrow \frac{A}{\sin \alpha}=\frac{B}{\sin \beta}=\frac{C}{\sin \gamma}</math>
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| ==See also==
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| * [[Law of sines]]
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| * [[Mechanical equilibrium]]
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| * [[Bernard Lamy (mathematician)]]
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| ==Further reading==
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| * R.K. Bansal (2005). "A Textbook of Engineering Mechanics". Laxmi Publications. p. 4. ISBN 978-81-7008-305-4.
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| * I.S. Gujral (2008). "Engineering Mechanics". Firewall Media. p. 10. ISBN 978-81-318-0295-3
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| [[Category:Statics]]
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| [[Category:Physics theorems]]
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39 year old Secondary College Teacher Dino Gohr from Fenelon Falls, likes to spend some time origami, diet and actions. Has completed a great around the world journey that consisted of traveling to the Pontcysyllte Aqueduct and Canal.