Playing with Lagrangian and I screw up

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    Lagrangian Screw
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SUMMARY

The discussion centers on the proper application of the Lagrangian method in classical mechanics, specifically regarding the treatment of the Lagrangian as an abstract function of independent variables. The participant emphasizes that one cannot prematurely solve the equations of motion and reinsert them into the Lagrangian. The correct approach involves transitioning from abstract equations to specific solutions only when solving the Euler-Lagrange equations, highlighting a common misunderstanding in the application of these concepts.

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  • Familiarity with Euler-Lagrange equations
  • Basic knowledge of kinetic energy concepts
  • Ability to interpret abstract mathematical functions
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  • Study the derivation and application of the Euler-Lagrange equations
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Lagrangian, Kinetic Energy (where am I going wrong)
I am sorry for all these questions this morning.

Could someone read the attached and tell me where I am going wrong?
 

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Trying2Learn said:
Summary:: Lagrangian, Kinetic Energy (where am I going wrong)

I am sorry for all these questions this morning.

Could someone read the attached and tell me where I am going wrong?
The Lagrangian approach requires that you treat the Lagrangian as an abstract function of independent variables. You can't jump ahead, solve the equations of motion, and plug these back into the Lagrangian and start again.

It's only when you are solving the Euler-Lagrange equations that you transition from the equations in their abstract form, to the equations that represent a specific solution in terms of a particle trajectory etc.

Text books tend to vary to the extent that they make this distinction clear.
 
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Ah ha!

Thank you!
 
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