Invariant quantities of a lagrangian?

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To determine invariant quantities from a Lagrangian, one must identify conserved quantities that arise from symmetries in the system. The discussion highlights that invariant quantities, such as momentum and energy, are linked to the invariance of the Lagrangian under transformations like rotations or translations. The Euler-Lagrange equations can be utilized to find these conserved quantities, particularly when a coordinate is cyclic, meaning it does not appear explicitly in the Lagrangian. The conversation also emphasizes the importance of understanding the definitions of invariance and conservation laws, suggesting resources like Landau's mechanics and Noether's theorem for deeper insights. Overall, the focus is on how symmetries in the Lagrangian lead to conservation laws in physical systems.
  • #31
The Lagrangian you got in polar coordinates can be simplified before you compute derivatives. Do that properly.
 

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