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. Nach dem Satz, {Anzeigestil {frac {EIN}{sin alpha }}={frac {B}{sin beta }}={frac {C}{sin gamma }}} wo ein, B and C are the magnitudes of the three coplanar, concurrent and non-collinear vectors, {Anzeigestil V_{EIN},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] Inhalt 1 Nachweisen 2 Siehe auch 3 Verweise 4 Further reading Proof As the vectors must balance {Anzeigestil V_{EIN}+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^{Ö}-Alpha ,180^{Ö}-Beta ,180^{Ö}-Gamma } . By the law of sines then[1] {Anzeigestil {frac {EIN}{Sünde(180^{Ö}-Alpha )}}={frac {B}{Sünde(180^{Ö}-Beta )}}={frac {C}{Sünde(180^{Ö}-Gamma )}}.} Then by applying that for any angle {Theta im Display-Stil } , {Displaystyle-Sünde(180^{Ö}-Theta )=sin theta } wir erhalten {Anzeigestil {frac {EIN}{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". Abgerufen 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 Kategorien: StaticsPhysics theorems