19

Classical Mechanics and Geometrical Optics

19.1 Fermat’s Principle and Maupertuis’ Principle

Equation 14.51 has the form of Hamilton’s principle of classical mechanics. We could then be tempted to conclude that Hamilton’s principle of mechanics corresponds to Fermat’s principle of optics. In fact, this is not quite true. The correct variational principle of mechanics with which Fermat’s principle can be related, is Maupertuis’ principle, or the principle of least action.15

Hamilton’s principle of classical mechanics is written as

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where L is the Lagrangian, xi are the generalized coordinates, t the time, and x˙k=dxk/dt. The Euler equations ...

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