Invariant quantities of a lagrangian?

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SUMMARY

This discussion focuses on determining invariant quantities from a given Lagrangian, specifically in the context of classical mechanics. Participants emphasize that invariant quantities are conserved quantities resulting from symmetries in the Lagrangian, such as energy and momentum. The Euler-Lagrange equation is highlighted as a crucial tool for identifying these conserved quantities, particularly under conditions of translational and rotational invariance. The conversation also references Landau's mechanics and Noether's theorem as foundational resources for understanding these concepts.

PREREQUISITES
  • Understanding of Lagrangian mechanics and the Euler-Lagrange equation
  • Familiarity with concepts of symmetry in physics
  • Knowledge of conserved quantities such as energy and momentum
  • Basic understanding of gauge transformations and their implications
NEXT STEPS
  • Study the Euler-Lagrange equation in detail to understand its application in finding conserved quantities
  • Explore Noether's theorem to grasp the relationship between symmetries and conservation laws
  • Investigate the implications of rotational symmetry on Lagrangian systems
  • Learn about the differences in applying Lagrangian mechanics in Cartesian versus cylindrical coordinates
USEFUL FOR

Students and professionals in physics, particularly those studying classical mechanics, theoretical physicists, and anyone interested in the principles of symmetry and conservation laws in Lagrangian systems.

  • #31
The Lagrangian you got in polar coordinates can be simplified before you compute derivatives. Do that properly.
 

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