Why Is Action Defined as Energy Minus Potential Energy in Physics?

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    Least action Principle
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Discussion Overview

The discussion centers around the definition of action in physics, specifically the expression of action as the difference between energy and potential energy (E-U). Participants are exploring the theoretical underpinnings and implications of this definition, as well as its connection to Newton's laws of motion.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant expresses confusion about why action is defined as E-U and seeks clarification.
  • Another participant mentions that setting the Lagrangian to T-V leads to the recovery of Newton's laws of motion, implying a connection between these concepts.
  • A further contribution questions why T-V recovers Newton's laws, suggesting that this is a topic worth exploring in more detail.
  • Links to additional resources are provided for further reading on the topic.

Areas of Agreement / Disagreement

The discussion does not appear to reach a consensus, as participants are still exploring the reasoning behind the definition of action and its implications.

Contextual Notes

Some assumptions about the definitions of terms like energy, potential energy, and the Lagrangian may be implicit in the discussion. The connection between the Lagrangian formulation and Newton's laws is mentioned but not fully resolved.

Who May Find This Useful

Individuals interested in theoretical physics, particularly those studying classical mechanics and the principles of Lagrangian mechanics.

Andrea2
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Hi! I'm new of this forum and I'm searching a way to understand why the action is E-U, but in this moment i don't know how to do...ther's someone who can help me? Thank you
 
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It turns out that if you set the Lagrangian to be T-V then you recover Newton's laws of motion.
 
Andrea2 said:
Hi! I'm new of this forum and I'm searching a way to understand why the action is E-U, but in this moment i don't know how to do...ther's someone who can help me? Thank you

The question is of course: why does T-V recover Newton's laws of motion? As it turns out: that question is not hard to answer.

An abbreviated discussion is in post https://www.physicsforums.com/showpost.php?p=2975435&postcount=10" of the recent thread called 'Lagrangian'.

A more detailed version (more diagrams) is available on my website: http://www.cleonis.nl/physics/phys256/least_action.php" .
 
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ok, thank you very much!
 

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