Lami's theorem

Lami's theorem In physics, Lami's theorem is an equation relating the magnitudes of three coplanar, concurrent and non-collinear vectors, which keeps an object in static equilibrium, with the angles directly opposite to the corresponding vectors. D'après le théorème, {style d'affichage {frac {UN}{sin alpha }}={frac {B}{sin beta }}={frac {C}{sin gamma }}} où un, B and C are the magnitudes of the three coplanar, concurrent and non-collinear vectors, {style d'affichage V_{UN},V_{B},V_{C}} , which keep the object in static equilibrium, and α, β and γ are the angles directly opposite to the vectors.[1] Lami's theorem is applied in static analysis of mechanical and structural systems. The theorem is named after Bernard Lamy.[2] Contenu 1 Preuve 2 Voir également 3 Références 4 Further reading Proof As the vectors must balance {style d'affichage V_{UN}+V_{B}+V_{C}=0} , hence by making all the vectors touch its tip and tail we can get a triangle with sides A,B,C and angles {displaystyle 180^{o}-alpha ,180^{o}-bêta ,180^{o}-gamma } . By the law of sines then[1] {style d'affichage {frac {UN}{péché(180^{o}-alpha )}}={frac {B}{péché(180^{o}-bêta )}}={frac {C}{péché(180^{o}-gamma )}}.} Then by applying that for any angle {thêta de style d'affichage } , {péché de style d'affichage(180^{o}-thêta )=sin theta } on obtient {style d'affichage {frac {UN}{sin alpha }}={frac {B}{sin beta }}={frac {C}{sin gamma }}.} See also Mechanical equilibrium Parallelogram of force Tutte embedding References ^ Jump up to: a b Dubey, N. H. (2013). Engineering Mechanics: Statics and Dynamics. Tata McGraw-Hill Education. ISBN 9780071072595. ^ "Lami's Theorem - Oxford Reference". Récupéré 2018-10-03. Further reading R.K. Bansal (2005). "A Textbook of Engineering Mechanics". Laxmi Publications. p. 4. ISBN 978-81-7008-305-4. I.S. Gujral (2008). "Engineering Mechanics". Firewall Media. p. 10. ISBN 978-81-318-0295-3 Catégories: StaticsPhysics theorems

Si vous voulez connaître d'autres articles similaires à Lami's theorem vous pouvez visiter la catégorie Physics theorems.

Laisser un commentaire

Votre adresse email ne sera pas publiée.


Nous utilisons nos propres cookies et ceux de tiers pour améliorer l'expérience utilisateur Plus d'informations