Explain the differential of lagrangian is a perfect ?L dt

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SUMMARY

The differential of the Lagrangian, denoted as dL, is established as a perfect differential in the context of classical mechanics. The relationship is defined by the equation dS = Ldt, where S represents the action. This definition is foundational and is supported by the properties of differentiable functions in the calculus of variations. The proof of its status as a perfect differential is inherently tied to these definitions and the mathematical framework surrounding them.

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  • Understanding of Lagrangian mechanics
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  • Knowledge of differential equations
  • Basic concepts of action in physics
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  • Study the calculus of variations in detail
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  • Learn about perfect differentials and their properties
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eman2009
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how we can explain the differential of lagrangian is a perfect ?L dt
 
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It's dS = Ldt, the action differential. It's just definitions.
 


yes, but how we can prove is it a perfect differential!
 


By definition - it is.
 

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