L=T+w? (Lagrangian dynamics)

In summary, while discussing dissipation systems, it was mentioned that some books define L as L=T+w. The question was raised if this definition is universal and where its limits lie. It was also asked about the definition of w, as it is not commonly seen in this form. It was explained that w represents the work done on the dynamical system, regardless of its dissipative nature. An example was requested for an expression of w in cases of dissipation. It was suggested that w can be included in Hamilton's Principle, where it represents the work of nonconservative forces acting on the system.
  • #1
enricfemi
195
0
while facing dissipation systems, some books define the L with L=T+w.
is it universal?
where is its limits?
THX!
 
Physics news on Phys.org
  • #2
How is w defined? I've never seen it written this way.
 
  • #3
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.
 
  • #4
So, can you give an example of an expression for w, when there is dissipation?
 
  • #5
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.
 
  • #6
i got it!

thanks Ben Niehoff and Dr.D.
 

What is L=T+w in Lagrangian dynamics?

L=T+w is a mathematical equation used in Lagrangian dynamics to describe the motion of a system. It represents the total kinetic energy (T) of the system plus the potential energy (w) of the system. It is derived from the principle of least action and is commonly used in classical mechanics and physics.

How is L=T+w used in Lagrangian dynamics?

L=T+w is used to determine the equations of motion for a system, based on the system's kinetic and potential energies. It is a more efficient method than using Newton's laws of motion, as it reduces the number of variables needed to describe the system's motion.

What is the significance of L=T+w in Lagrangian dynamics?

L=T+w is significant in Lagrangian dynamics because it simplifies the equations of motion for a system. It also allows for the use of generalized coordinates, making it easier to analyze and solve complex systems.

Can L=T+w be applied to any type of system?

Yes, L=T+w can be applied to any type of system, including mechanical, electrical, and even quantum systems. As long as the system's kinetic and potential energies can be defined, L=T+w can be used to describe the system's motion.

Is L=T+w a fundamental equation in physics?

No, L=T+w is not a fundamental equation in physics. It is derived from the principle of least action, which is a fundamental concept in classical mechanics. However, L=T+w has proven to be a powerful tool in analyzing and solving complex systems in various fields of physics.

Similar threads

Replies
3
Views
855
Replies
25
Views
1K
Replies
2
Views
125
  • Mechanics
Replies
1
Views
592
Replies
7
Views
718
  • Mechanics
Replies
2
Views
517
Replies
5
Views
815
  • Mechanics
Replies
3
Views
909
Replies
20
Views
8K
Replies
3
Views
2K
Back
Top