What Are Examples of Lagrangians in Various Disciplines?

[JTC]

Assuming generlized variables, q, we have a Lagrangian in mechanics as the kinetic energy, K, minus potential energy, U, with a dependency form such that

L(q,dq/dt) = K(q, dq/dt) - U(q)

Can someone provide examples of Lagrangians in other disciplines?

 

[PeroK]

What do you mean by other disciplines?

 

[JTC]

What do you mean by other disciplines?

I VAGUELY recall a Lagrangian in particle physics that was about a page long.

Just other examples of Lagrangians...

 

[PeroK]

I VAGUELY recall a Lagrangian in particle physics that was about a page long.

Just other examples of Lagrangians...

There must be lots on line. In General Relativity, for example:

https://en.wikipedia.org/wiki/Relativistic_Lagrangian_mechanics

Electromagnetism as well. They are almost everywhere.

 

[robphy]

Circuit Theory
https://physics.stackexchange.com/questions/351860/lagrangian-method-for-an-lc-circuit
http://www.site.uottawa.ca/~rhabash/ELG4152L10.pdf
https://arxiv.org/abs/1610.03438

Economics
https://www.bauer.uh.edu/rsusmel/phd/MR-15.pdf
see 82.2.3 Euler-Lagrange equation in
http://www2.gsu.edu/~mgtshi/Chapter 82 - Application of ODE in FER-April 2009.pdf
see p. 110 in
https://onlinelibrary.wiley.com/doi/pdf/10.1111/j.1524-4733.2006.00088.x

 

[jtbell]

I VAGUELY recall a Lagrangian in particle physics that was about a page long.

An example of a much simpler Lagrangian of that type, which is often taught as a stepping-stone to quantum field theory:

Classical Scalar Field in Four Dimensions

Here we use not the Lagrangian of an entire system, but rather the Lagrangian density at each spacetime point.