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.
are the magnitudes of the three coplanar, concurrent and non-collinear vectors,
, which keep the object in static equilibrium, and
α , β , γ
are the angles directly opposite to the vectors,[1] thus satisfying
α + β + γ =
Lami's theorem is applied in static analysis of mechanical and structural systems.
The theorem is named after Bernard Lamy.
[2] As the vectors must balance
, hence by making all the vectors touch its tip and tail the result is a triangle with sides
α , β , γ
are the exterior angles).
By the law of sines then[1]
Then by applying that for any angle
− θ ) = sin θ
(supplementary angles have the same sine), and the result is
sin α
sin β
sin γ