Lagrangian remains invariant under addition

  • Thread starter preet0283
  • Start date
  • #1
19
0

Main Question or Discussion Point

what is the reason that the lagrangian remains invariant under addition of an arbtrary function of time???
 

Answers and Replies

  • #2
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
MalleusScientiarum
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.
 

Related Threads for: Lagrangian remains invariant under addition

Replies
1
Views
567
  • Last Post
2
Replies
30
Views
3K
  • Last Post
Replies
16
Views
3K
Replies
4
Views
737
Replies
1
Views
908
Replies
3
Views
1K
Replies
2
Views
580
Top