How to derive Nielsen equation from Lagrange equation?

Click For Summary

Discussion Overview

The discussion revolves around the derivation of the Nielsen equation from the Lagrange equation, focusing on the theoretical aspects and the challenges faced in understanding the derivation process.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant expresses uncertainty about the origin of the commutator in the derivation and questions its relation to the Poisson bracket.
  • Another participant suggests that the initial resource found was insufficient and proposes looking at an alternative source for better clarity.
  • Clarification is provided regarding the notation of the commutator, emphasizing the order of operations involved.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the derivation process, with multiple viewpoints and uncertainties remaining regarding the commutator and the relationships involved.

Contextual Notes

Limitations include unclear definitions of terms like the commutator and the specific relationships referenced, as well as unresolved steps in the derivation process.

AlephClo
Messages
32
Reaction score
1
How to derive Nielsen equation from Lagrange equation
 
Physics news on Phys.org
Isn't google your friend ? What did you find so far ?
 
I have done couple hours of research and tried to derive it myself. The best that I found is this, but I do not understand where the commutator come from. It does not seem to be the Poisson braket commutator applied to T either (A,B) = AB-BA . Nor that I understand where the (2) relationship comes from. Thank you

upload_2019-1-9_5-4-47.png
 

Attachments

  • upload_2019-1-9_5-4-47.png
    upload_2019-1-9_5-4-47.png
    12.7 KB · Views: 3,564
AlephClo said:
The best that I found is this
It was the first one I found too. But: Not good enough then, ... (*)
What about the second one in the list I got ?

:smile: Except where it says ##=0## one should read ## = Q_j##

(*) And yes, the commutator [A,B] means: first B then A minus first A then B.
 
Thank you BvU.
 

Similar threads

Undergrad Requirement of Holonomic Constraints for Deriving Lagrange Equations
  • · Replies 1 ·
Replies
1
Views
1K
Undergrad Linearization of Lagrange equations
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Standard designation for generalization of Euler-Lagrange?
  • · Replies 5 ·
Replies
5
Views
2K
Graduate H-Theorem and Lagrange multipliers
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad Action in Lagrangian Mechanics
  • · Replies 5 ·
Replies
5
Views
2K
Graduate Lagrangian to the Euler-Lagrange equation
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Delta x in the derivation of Lagrange equation
  • · Replies 2 ·
Replies
2
Views
1K
Graduate Partial Differentiation in Lagrange's Equations
  • · Replies 7 ·
Replies
7
Views
3K
Undergrad Calculus in the derivation of Euler-Lagrange equation
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Discrete Euler-Lagrange equations
  • · Replies 3 ·
Replies
3
Views
3K