physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...

, Lami's theorem is an equation relating the magnitudes of three coplanar,

concurrent Concurrent means happening at the same time. Concurrency, concurrent, or concurrence may refer to: Law * Concurrence, in jurisprudence, the need to prove both ''actus reus'' and ''mens rea'' * Concurring opinion (also called a "concurrence"), a ...

and non-collinear vectors, which keeps an object in

static equilibrium In classical mechanics, a particle is in mechanical equilibrium if the net force on that particle is zero. By extension, a physical system made up of many parts is in mechanical equilibrium if the net force on each of its individual parts is zero ...

, with the angles directly opposite to the corresponding vectors. According to the theorem, :

\frac=\frac=\frac

where ''A'', ''B'' and ''C'' are the magnitudes of the three coplanar, concurrent and non-collinear vectors,

V_A, V_B, V_C

, which keep the object in static equilibrium, and ''α'', ''β'' and ''γ'' are the angles directly opposite to the vectors. : Lami's theorem is applied in static analysis of mechanical and structural systems. The theorem is named after

Bernard Lamy Bernard Lamy (15 June 1640 – 29 January 1715) was a French Oratorian, mathematician and theologian. Life Lamy was born in Le Mans, France. After studying there, he went to join the Maison d'Institution in Paris, and to Saumur thereafter. I ...

Proof

As the vectors must balance

V_A+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

180^o -\alpha, 180^o -\beta, 180^o -\gamma

. By the law of sines then

\frac=\frac=\frac.

Then by applying that for any angle

\theta

\sin (180^o - \theta) = \sin \theta

we obtain

\frac=\frac=\frac.

Proof

See also

References

Further reading