Question: How calculate the Skyrme of motion from the Lagrangian density in maple using the physics package?

How can I calculate the Euler-Lagrange equation from the Lagrangian density from Gauged Baby Skyrme model in maple using the physics package? Here, the rules of the operation in the inner space are the same that of the vectors conventional: dot and cross products, etc...
Following below the Lagrangian density.

Errata:

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