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. According to the theorem,
where are the magnitudes of the three coplanar, concurrent and non-collinear vectors, , which keep the object in static equilibrium, and are the angles directly opposite to the vectors,[1] thus satisfying .
Lami's theorem is applied in static analysis of mechanical and structural systems. The theorem is named after Bernard Lamy.[2]
Proof
[edit]As the vectors must balance , hence by making all the vectors touch its tip and tail the result is a triangle with sides and angles ( are the exterior angles).
By the law of sines then[1]
Then by applying that for any angle , (supplementary angles have the same sine), and the result is
See also
[edit]References
[edit]- ^ a b Dubey, N. H. (2013). Engineering Mechanics: Statics and Dynamics. Tata McGraw-Hill Education. ISBN 9780071072595.
- ^ "Lami's Theorem - Oxford Reference". Retrieved 2018-10-03.