Discover the Lagrangian for 2D Vortices | Essential Homework Equations

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SUMMARY

The discussion centers on finding the Lagrangian for 2D vortices, clarifying that a Lagrangian describes the equations of motion for a specific system rather than being exclusive to vortices. It emphasizes that vortices are solutions to the equations of motion and suggests that users should specify the system exhibiting vortex behavior to derive the appropriate Lagrangian. An example of a system with vortex solutions is provided, such as a smoke ring.

PREREQUISITES
  • Understanding of Lagrangian mechanics
  • Familiarity with fluid dynamics and vortex behavior
  • Knowledge of equations of motion
  • Basic concepts of classical mechanics
NEXT STEPS
  • Research specific systems that exhibit vortex solutions, such as fluid flows or plasma physics.
  • Study the derivation of the Lagrangian for classical systems using examples like smoke rings.
  • Explore the mathematical formulation of equations of motion in Lagrangian mechanics.
  • Learn about the role of vortices in different physical systems and their implications in fluid dynamics.
USEFUL FOR

Students of physics, particularly those studying classical mechanics and fluid dynamics, as well as researchers interested in vortex dynamics and Lagrangian formulations.

Alireza383
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Homework Statement



Hello,
Do you know how to find Lagrangian for 2D Vortices?

Homework Equations

The Attempt at a Solution

 
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Welcome to the forum.

You are going to want to read the notes on here about how to post. Because you are posting in a homework help forum you need to follow certain rules.

A vortex is a solution to equations of motion. A Lagrangian is a way of expressing the equations of motion for a particular system. That is, you are putting things a bit out of order. A Lagrangian is not "for 2D vortices." It is the Lagrangian of a certain system, and some systems happen to have vortex solutions.

Maybe you meant: Can we name a system that exhibits vortices? And what is the Lagrangian for that system? And how can one calculate a vortex in that system?

First part is easy, if you count a smoke ring as a vortex.



For the rest, you should go back and ask your question correctly.
 

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