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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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    $\begingroup$ This question appears to be off-topic because it is about what tools engineers (not physicists) choose to use. $\endgroup$
    – user10851
    Jul 5, 2013 at 21:45

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In civil engineering they use it for structures, and strength of materials in the elastic realm. It goes by the name of the enegy method. Google books might give an indication.

Some authors are Beer and the mechanical engineer Stephen Timoshenko.

This is for some what "static" indeterminant structures. So, there is no time element. But, I am sure it could be used dynamicaly for seismic analysis. The structures have virtual loads or displacements applied to them and you get the complimentry diplacement (for load) or load (for displacement) as a result.

It is an elegant use. It can also be applied to warping of beams.

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  • $\begingroup$ Hi qwerty and welcome to Physics.SE! This seems to be part answer and part question. Note that "personal" phrases like "I'm interested in this, too" or "I have the same question" are discouraged here, as they are not fit for our Q&A format. Otherwise, have fun! $\endgroup$
    – ACuriousMind ♦
    Aug 20, 2014 at 1:12
  • $\begingroup$ @ACuriousMind true, though I've now edited that part out. $\endgroup$
    – David Z
    Aug 20, 2014 at 2:52
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I'm a electrical engineer, and have never used either one in over 30 years of designing circuits. I vaguely remember that we went over them briefly in school, but since I haven't used them (knowingly) since, I can't tell you what the physical meaning of either is, which of course perpetuates the fact that I'm not going to use them.

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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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    $\begingroup$ For static problems engineers use Strain Energy (see Castigliano's method). You might call it negative lagrangian. $\endgroup$
    – John Alexiou
    Jul 5, 2013 at 14:36
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Yes lagrangians and hamiltonians are indeed used by engineers.

To be precise, used by some types of engineers like aeronautical engineers, aerodynamics etc..

For example: http://www.osti.gov/eprints/topicpages/documents/starturl/47/566.html

As far as i know electrical engineers dont use the lagrangian nor hamiltonian forms of mechanics nor electromagnetism.

P.S. I have studied electrical engineering and the only Hamiltonian formalism we officially encountered was in Control Theory.

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  • $\begingroup$ The link is dead. Do you have the title of the article? $\endgroup$
    – Cheng
    Jun 9, 2022 at 0:37
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    $\begingroup$ @Cheng, unfortunately I have no idea which post it was, but it was some engineering paper (aeronautical engineering if i remember correctly), using lagrangians, simply as a an example. I am sure you can find more $\endgroup$
    – Nikos M.
    Jun 9, 2022 at 5:41