Lami's theorem

In physics, Lami's theorem is an equation relating the magnitudes of three coplanar, concurrent and non-collinear force vectors, which keeps an object in static equilibrium, with the angles directly opposite to the corresponding vectors. According to the theorem, v A sin ⁡ α = v B sin ⁡ β = v C sin ⁡ γ {\displaystyle {\frac {v_{A}}{\sin \alpha }}={\frac {v_{B}}{\sin \beta }}={\frac {v_{C}}{\sin \gamma }}} where v A , v B , v C {\displaystyle v_{A},v_{B},v_{C}} are the magnitudes of the three coplanar, concurrent and non-collinear vectors, v → A , v → B , v → C {\displaystyle {\vec {v}}_{A},{\vec {v}}_{B},{\vec {v}}_{C}} , which keep the object in static equilibrium, and α , β , γ {\displaystyle \alpha ,\beta ,\gamma } are the angles directly opposite to the vectors, thus satisfying α + β + γ = 360 o {\displaystyle \alpha +\beta +\gamma =360^{o}} . Lami's theorem is applied in static analysis of mechanical and structural systems. The theorem is named after Bernard Lamy.