the 2 lagrangians


by sjarel
Tags: lagrangians
sjarel
#1
Nov4-06, 03:37 PM
P: n/a
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

Phys.Org News Partner Physics news on Phys.org
Physicists design quantum switches which can be activated by single photons
'Dressed' laser aimed at clouds may be key to inducing rain, lightning
Higher-order nonlinear optical processes observed using the SACLA X-ray free-electron laser

Register to reply

Related Discussions
Lagrangians and P-Conservation Advanced Physics Homework 2
the 2 lagrangians General Physics 0
Quantum mnechanics with lagrangians?... Quantum Physics 2
Quantization without Lagrangians. General Physics 19