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Analytical Mechanics (Lagrangian and Hamiltonian) are useful in Physics (e.g. in Quantum Mechanics) but are they also used in application, by engineers? For example, are they used in designing bridges or buildings?

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This question appears to be off-topic because it is about what tools engineers (not physicists) choose to use. –  Chris White Jul 5 '13 at 21:45
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I'm not an engineer myself, but as far as I know, Lagrangians and Hamiltonians have their use in complicated but calculable situations. In order to solve the e.o.m. for a bridge or so, most engineers rely on specific programs for exactly such a purpose that calculate the statics using Newtonian mechanics and a finite element approach.

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For static problems engineers use Strain Energy (see Castigliano's method). You might call it negative lagrangian. –  ja72 Jul 5 '13 at 14:36
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