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

AI Thread Summary
The discussion centers on the definition of L in Lagrangian dynamics as L=T+w, particularly in the context of dissipative systems. Participants question the universality of this definition and seek clarification on the limits of its application. The term "w" is defined as the work done on the dynamical system, applicable to both dissipative and non-dissipative cases. An example of "w" in a dissipative context is requested, emphasizing its representation of work done on the system. The conversation highlights Hamilton's Principle as a method to incorporate nonconservative forces into the equations of motion.
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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