Question

Does a Lagrangian being independent to a spacial coordinate imply spatial translation symmetry?

Answer 1

Hey mate

Here is your answer

Yes Lagrangian being independent to a spatial coordinate imply spatial translation symmetry.

They is because the Lagrangian, which in some respects represents the path of the motion.

Answer 2

Hey !

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The area-weighted approach preserves spherical symmetry on an equal-angle polar grid for 1D radial flows, but it does not satisfy the GCL.

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Thanks !