Room Temp Super Conductors HONEST!
Stellar Black Holes - Some Myths

Solving the simple pendulum question.

From my previouse post “The Legrangian - How it’s used…” I had a left over question, which was to solve the legrangian equation of motion:

\frac {d}{dt} \frac {\delta L} {\delta \dot q} = \frac {\delta L} {\delta q}

So starting with what we had last time:

L = \frac {1}{2} I \centerdot \theta^2 + mgl\cos\theta

We can find:

I=ml^2 For a simple pendulum (I is the moment of inertia).

\frac {\delta L} {\delta q} = -mgl\sin\theta

\frac {\delta L} {\delta \dot q} = \frac {2}{2}ml^2\dot\theta = ml^2\dot\theta

\frac {d}{dt} \frac {\delta L} {\delta \dot q} = ml^2\ddot\theta

-mgl\sin\theta = ml^2\ddot\theta

\frac {-mgl\sin\theta} {ml^2} = \ddot\theta

\frac {-g\sin\theta} {l} = \ddot\theta

The solution to the equation of motion, if you want to find velocity or position you can just integrate. Easy!

This entry was posted on Friday, March 21st, 2008 at 12:28 am and is filed under classical physics. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.

3 Responses to “Solving the simple pendulum question.”

  1. NeonBlack Says:
    March 21st, 2008 at 2:07 am

    I think it’s spelled Lagrangian. And you make it sound easier than it is. You can’t directly integrate this. To solve the equation of motion you’d typically make a small angle approximation at this point. I see people all the time who get to this point and then say easy, just integrate! And then sit there, not knowing what to do.
    Also if you set this in tex, I think you can make partial d’s with \partial.

  2. NeonBlack Says:
    March 21st, 2008 at 2:18 am

    The previous post is excellent though.

  3. Klaynos Says:
    March 21st, 2008 at 11:49 am

    Thanks NeonBlack, I know that the integration is non-trivial the easy bit is an in joke with some friends that I included just because well, I forgot that this was a blog and not a message to one of them.

    I’ll probably go through the integrating in a later post, but didn’t have time when I wrote the post last night…. Dissertation writing season! I dunno why I use \delta instead of \partial…

    Thanks…

Leave a Reply

You must be logged in to post a comment.

This blog proudly hosted by ScienceForums.Net Blogs. Subscribe to our RSS Logo global RSS feed.