Is L=T+w a Universal Definition in Lagrangian Dynamics for Dissipation Systems?

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Discussion Overview

The discussion revolves around the expression L=T+w in the context of Lagrangian dynamics, particularly for systems experiencing dissipation. Participants explore the definition of work (w) and its applicability within this framework, questioning whether this formulation is universally accepted and identifying its limitations.

Discussion Character

  • Debate/contested
  • Technical explanation

Main Points Raised

  • Some participants inquire about the universality of the expression L=T+w in the context of dissipation systems.
  • There is a request for clarification on the definition of w, with one participant stating it represents the work done on the dynamical system, applicable to both dissipative and non-dissipative scenarios.
  • Another participant asks for an example of how w is expressed in the presence of dissipation.
  • A participant mentions that they have not encountered the expression in finite form but expects w to denote the work done on the system.
  • Hamilton's Principle is referenced, suggesting that work (W) from various forces is integrated into the equations of motion for nonconservative forces.

Areas of Agreement / Disagreement

Participants express uncertainty regarding the universal acceptance of the L=T+w formulation and the definition of w, indicating that multiple competing views remain on these topics.

Contextual Notes

There are limitations in the discussion regarding the definitions of terms and the specific conditions under which the expression L=T+w is applicable, as well as the unresolved nature of how w is formulated in dissipative contexts.

enricfemi
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while facing dissipation systems, some books define the L with L=T+w.
is it universal?
where is its limits?
THX!
 
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How is w defined? I've never seen it written this way.
 
Ben Niehoff said:
How is w defined? I've never seen it written this way.

w is the work done on the dynamical system, on matter whether it is dissipative or not.
 
So, can you give an example of an expression for w, when there is dissipation?
 
I've never seen it written in finite form like that, but I would expect that w to represent the work done on the system.

Hamilton's Principle can be written as
int(variation of (T*) + variation(W))dt = 0
where that W is the work of the several forces acting on the system. This is the way that nonconservative forces are included into the formulation of the system equations of motion.
 
i got it!

thanks Ben Niehoff and Dr.D.
 

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