Hey everyone,
From documentation I see sympy has a tensor package (awesome) and I
see some discussion on being able to calculate Eular-Lagrange equations.
However, I was wondering if sympy can calculate tensor based Euler-Lagrange
equations of motion.
For, example, let's take the example of electricity and magnitism [1].
Here our Lagrangian = 1/4 F_uv F^uv - A_a J^a. Here F_uv is the maxwell
tensor, A_a is the E&M vector potential and J^a is the source of that
potential. Varying this action with respect A_a gives:
d(F^uv)dx_u = J^v, the standard E&M equation of motion. See the wikipedia
link below for a better description.
Does anyone know if sympy is equipped to handle tensor based
Eular-Lagrange equations equations such as these? If so, how would I go
about solving for this E&M example? Thanks.
[1]
http://en.wikipedia.org/wiki/Covariant_formulation_of_classical_electromagnetism#Lagrangian_for_classical_electrodynamics
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