Lagrangian remains invariant under addition

  • Thread starter preet0283
  • Start date
  • #1
preet0283
19
0
what is the reason that the lagrangian remains invariant under addition of an arbtrary function of time?
 

Answers and Replies

  • #2
rayveldkamp
60
0
Hi,
It is the equations of motion that are invariant under the addition of a function that is the total time derivative of some function, to the Lagrangian. Since the Euler-Lagrange equations involve derivatives with respect to position and velocity only, a partial derivative wrt to position or velocity of this added function will be zero.
Hope this helps

Ray
 
  • #3
Preet, what you just noticed is the basis for later things like contact transformations and the resulting Hamilton-Jacobi theory. It turns out that you can add a more general class of functions whose derivatives obey a certain relationship, and if you can find these functions and changes of variable then you can make any classical physics problem a piece of cake.
 

Suggested for: Lagrangian remains invariant under addition

  • Last Post
Replies
20
Views
828
  • Last Post
Replies
2
Views
262
  • Last Post
Replies
1
Views
265
Replies
30
Views
633
Replies
6
Views
549
  • Last Post
Replies
32
Views
953
  • Last Post
Replies
5
Views
490
Replies
5
Views
396
Replies
41
Views
1K
Top