Virtual differentials approach to Euler-Lagrange eqn - necessary?

In summary, the conversation is about the struggle to understand the d'Alembert-based virtual differentials derivation for E-L in intermediate mechanics. The use of 'pretend' differentials over a time interval of zero is not sinking in for the speaker and they are questioning its necessity. They wonder if they can skip this approach and still understand Hamilton's principle. The other person in the conversation suggests that it is not necessary to learn this approach and shares their own experience with not covering it in their intermediate mechanics course. However, they also mention that it can be a useful approach for understanding forces associated with constraints on a system. They invite others who are more knowledgeable to contribute to the conversation and encourage the speaker to enjoy learning mechanics.
  • #1
fgarnold
1
0
I'm currently teaching myself intermediate mechanics & am really struggling with the d'Alembert-based virtual differentials derivation for E-L. The whole notion of, and justification for, using 'pretend' differentials over a time interval of zero just isn't sinking in with me. And I notice that not all textbook authors invoke it, so I'm wondering how necessary it is, given that Hamilton's principle gets us to E-L just fine.
So, will I ever need this virtual displacement/work approach for something other than a route to E-L, or can I safely wave bye-bye to it?
Thx.
 
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  • #2
There is nothing wrong with skipping this if it is your first time through Lagrangian/Hamiltonian dynamics. When I took intermediate mechanics we did not cover the virtual displacement/work stuff. We used what was the standard book at the time - Marion and Thornton - which didn't even cover it. However, the honors version of the course did cover it. I have never learned it, but recently have started to re-learn mechanics just for fun and plan on going through the virtual displacement stuff this time around. It appears that it can be a useful approach to getting a nice physical picture of the forces associated with constraints on a system.

Perhaps one of the many people around here that know much more about this than I do will chime in.

Enjoy,

jason
 

Related to Virtual differentials approach to Euler-Lagrange eqn - necessary?

1. What is the virtual differentials approach to Euler-Lagrange equations?

The virtual differentials approach is a method used in classical mechanics to find the equations of motion for a system. It involves considering small variations in the system's coordinates and velocities, known as virtual displacements and virtual velocities, and finding the conditions that must be satisfied for the system to be in equilibrium.

2. How is the virtual differentials approach different from the traditional approach?

In the traditional approach, the equations of motion are derived by considering the system's total energy and using the principle of least action. The virtual differentials approach, on the other hand, focuses on the individual forces acting on the system and uses the principle of virtual work to derive the equations of motion.

3. Why is the virtual differentials approach necessary?

The virtual differentials approach is necessary because it allows for a more intuitive understanding of the forces and constraints acting on a system. It also allows for a more general and flexible approach to solving problems in classical mechanics.

4. Are there any limitations to the virtual differentials approach?

Like any method, the virtual differentials approach has its limitations. It may not be suitable for more complex systems with non-conservative forces or constraints. It also assumes that the system is in equilibrium, which may not always be the case.

5. How is the virtual differentials approach applied in real-world scenarios?

The virtual differentials approach is commonly used in engineering and physics to model and analyze the behavior of mechanical systems. It has applications in a wide range of fields, including robotics, aerospace, and structural engineering.

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