Lagrangian & Noether's thm

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quasar987

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I have this question here from last year's exam that goes

"Use Noether's theorem to show that the angular momentum is conserved when the lagrangian is invariant under rotations."

I just want to know if this is true in the most general case, or if there are some restrictions somewhere not mentioned in the question.

Thank you.
 
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  • #2
Yes, you'd have to check for infinitesimal rotations.
 

What is the Lagrangian?

The Lagrangian is a mathematical function that describes the dynamics of a physical system. It takes into account the kinetic and potential energies of the system and is used to derive the equations of motion for the system.

What is Noether's theorem?

Noether's theorem is a fundamental principle in physics that states that for every continuous symmetry in a physical system, there exists a corresponding conservation law. In other words, if a physical system remains unchanged under certain transformations, then there must be a corresponding quantity that remains constant in the system.

How are Lagrangian and Noether's theorem related?

Lagrangian and Noether's theorem are closely related because the Lagrangian is used to derive the equations of motion for a physical system, which can then be used to identify symmetries in the system. These symmetries can then be used to apply Noether's theorem and determine the corresponding conservation laws.

What are some real-world applications of Lagrangian and Noether's theorem?

Lagrangian and Noether's theorem have many applications in physics, particularly in classical mechanics and field theory. They are used to describe the motion of particles, analyze the behavior of physical systems, and determine conservation laws in various contexts such as electromagnetism and general relativity.

Are there any limitations to Lagrangian and Noether's theorem?

While Lagrangian and Noether's theorem are powerful tools in physics, they do have some limitations. For example, they may not be applicable to systems with non-conservative forces or systems with non-uniform potentials. Additionally, Noether's theorem only applies to continuous symmetries, so it may not be applicable in all physical systems.

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