the 2 lagrangians

sjarel

I just found Max's question on the 2 Lagrangians giving the same EOM's
(8 Mar 06).

[ Mod. note: The poster is probably referring to the message

news:1141408564.026625.242830@u72g2000cwu.googlegroups.com
http://groups.google.ca/group/sci.ph...dbe8734370c10d

Please quote when replying. -ik ]

As I didn't see a reaction , here is one .....

Using the identity (x+y)^2 = x^2 + y^2 - 2 x y

the 2 Lagrangians are connected by
F = m/2 (dx - dy)^2 -a/2 (x - y) ^2
where dX stands for x_dot.

It is easy to see that F is the difference between the energy
(hamiltonian) of the two formulations.
F = H - H' , hence F = d [ (H - H') t] and the text-book
property is satisfied.

Sjarel