A New World
My ramblings about science….

Well I’m stuck in uni for a little while before my tutorial starts at 1, so I thought I’d quickly explain how the Lagrangian is used.

After deciding on your coordinate system, which can really be quite arbitary, you need to write down 2 things in this coordinate system.

Firstly the kinetic energy, which for our pendulum example (length l) in my first post about this would be something like:

Where I is the moment of inertia for the system.

Secondly we require an equation for the potential energy, this is more difficult in this case as we need to work out how the height change for a given theta.

Now it should have been noted by anyone who’s studied much physics that I’ve failed to draw a diagram up to this point. And the diagram that will appear attached to this post was/will be done when I got/get home. But I do have one I just drew infront of me. And from this using a bit of simple trig I can show that:

Which gives:

The next step is finding the Lagrangian, but that is trivially:

L = T - U

=>

So all that is left is to put this through the equation of motion.

The easiest way to do this is to work out the two partial derrivatives first, and then put them into the equation.

I’ll leave this as an exercise, feel free to message me your answers or post queiers in the comments… Answers in comments will be deleted

This entry was posted on Tuesday, February 12th, 2008 at 11:48 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.