Register to reply

Susskind's theoretical minimum

Share this thread:
43arcsec
#1
Jan3-14, 06:19 PM
P: 7
If anyone out there has worked through Susskind's book, I have two questions on the Lagrangian to Hamiltonian section, any help would be greatly appreciated:

1) In Lecture 8 exercise 2, he wants you to calculate take the Lagrangian of

L=1/2ω d/dt q - ω/2 q^2 as a Hamiltonian and says it equals (ω=sqrt(k/m) )

H=ω/2 ( p^2 + q^2)

From what I can tell from his book, the Lagrangian is kinetic energy - potential energy, while the Hamiltonian is kinetic energy plus the potential energy.

I've tried making this work every which way but couldn't come up with it.

Also, on the next page (158) he says the Lagrangian is (d/dt)^2 q = - ω q

This is just the equation of motion for a harmonic oscillator; how does this pass for a Lagragian that is supposed to be the K.E - P.E.?

Sorry if I'm missing something easy, but thanks for taking a look.

-Marc
Phys.Org News Partner Physics news on Phys.org
Cool calculations for cold atoms: New theory of universal three-body encounters
New method for non-invasive prostate cancer screening
How bubble studies benefit science and engineering
maajdl
#2
Jan4-14, 03:03 PM
PF Gold
P: 377
First, I think L is maybe given by:

L=1/2ω (d/dt q)^2 - ω/2 q^2

From there, you can begin to calculate p = dL/d(qp) where qp = d/dt q .
Result follows immediately.
43arcsec
#3
Jan4-14, 03:35 PM
P: 7
Canonical momentum, of course. Thanks Maajdl, I am in your debt.


Register to reply

Related Discussions
A Theoretical Minimum | Looking for Guidance Academic Guidance 4
Good follow up to The theoretical Minimum? Academic Guidance 3
Intro Physics The Theoretical Minimum by Susskind and Hrabovsky Physics & Astro Textbook Listings 2
The Theoretical Minimum, Released today, January 29th 2013 Science & Math Textbooks 21
Landau's Theoretical Minimum General Discussion 6