The Theoretical Minimum: What You Need to Know to Start Doing Physics by Leonard Susskind & George Hrabovsky

Author:Leonard Susskind & George Hrabovsky [Susskind, Leonard]
Language: eng
Format: mobi
ISBN: 9780465031740
Publisher: Basic Books
Published: 2013-01-28T23:00:00+00:00

The notation for generalized momentum is pi.

With that definition, the Euler-Lagrange equations are

Let’s do a couple of examples starting with a particle in polar coordinates. In this case the qi’s are the radius, r, and the angle, θ. We can use the result from Exercise 4 to get the Lagrangian:

The generalized momentum conjugate to r (the r momentum) is

and the corresponding equation of motion is

Using and canceling m from both sides, we can write this equation in the form

The equation of motion for the angle θ is especially interesting. First consider the conjugate momentum to θ:

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.