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. According to the theorem,

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

Proof

As the vectors must balance , hence by making all the vectors touch its tip and tail the result is a triangle with sides A, B, C and angles

By the law of sines then[1]

Then by applying that for any angle , , and the result is

See also

References

  1. Dubey, N. H. (2013). Engineering Mechanics: Statics and Dynamics. Tata McGraw-Hill Education. ISBN 9780071072595.
  2. "Lami's Theorem - Oxford Reference". Retrieved 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
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