Abstract
The third chapter covers the first integral and the variational principle. The notions of cyclic coordinates and Poisson brackets are first recalled. The Theorem of Poisson, Euler equation, and the variational principle are then addressed. An application in optics, namely the Fermat principle, is reviewed. Five exercises are then solved, namely on the Watt Regulator, on the first integral of a free material point, on the brachistochrone problem, on the minimum surface of revolution, and on optical paths and Fermat principle.
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