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He worked on applied topics such as engineering, elasticity and fluid mechanics. He made contributions to Fourier series and their application. He gave the well known Navier-Stokes equations for an incompressible fluid in 1821. In 1822 he gave equations for viscous fluids.
A specialist in road and bridge building, he was the first to devlop a theory of suspension bridges which before then had been built to empirical principles.
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