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

[enricfemi]

while facing dissipation systems, some books define the L with L=T+w.
is it universal?
where is its limits?
THX!

 

[Ben Niehoff]

How is w defined? I've never seen it written this way.

 

[enricfemi]

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.

 

[Ben Niehoff]

So, can you give an example of an expression for w, when there is dissipation?

 

[Dr.D]

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.

 

[enricfemi]

i got it!

thanks Ben Niehoff and Dr.D.