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Variational Mechanics


pulkit
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  • 2 months later...

Most of Lagrangian mech applications I do are implemented via energy principles, and actually are pretty identical to principles such as the principle of virtual work or virtual power (equilibrium stuff). I think the mathematical constructs have some added value in comparison to other stuff if you're working for example with dynamics problems or need to include something with similar mathematical aspects, like optimization using numerical methods etc. The math is really elegant, though.

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Lagrangian mechanics is fundamental to quantum field theory too. In fact, all of the modern high energy theories are described by Lagrangians (of more precisely, Lagrange densities). This is mainly because the Path Integral formalism of QFT weights each possible 'path' between initial and final conditions with the expenential of the action required for the path. The prefered path is then the one with the least action.

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  • 2 weeks later...

Having studied Lagrangian mechnics somewhat by now, I must say I didn't understand the mathematical derivations used, but the methods of applications were mostly very mechanical and the differential equations obtained in the end did not seem humanly solvable.

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