Simple Lagrangian mechanics problem.

[Lavabug]

Homework Statement

See image (I think I forgot to rotate it, careful with your necks!):
http://img600.imageshack.us/img600/7888/p1000993t.jpg

The system consists of 2 point masses joined by a rigid massless bar of length 2l, which can rotate freely only in the z-x plane. The center of the bar is attached to a spring with constant k, natural length delta, which remains along the OY axis. Gravity acts down along the z-axis. Find the Lagrangian and the canonical equations of motion

The Attempt at a Solution

Just wanted to check if my solution looks correct, I identified 2 generalized coordinates total.

 

[Mindscrape]

Your set up looks fine to me, though I didn't actually check your differentiation. You should have 2 generalized coordinates: one from the bar because the bar is rigid, and another from the spring. What you need to ask yourself is, what are some limits I can take, what do I expect from the limits, and what do the limits from your equations actually give? For example, in the case that mass 2 is much bigger than mass 1, what physical system do you now have, and do your equations support it?

 

[Lavabug]

Your set up looks fine to me, though I didn't actually check your differentiation. You should have 2 generalized coordinates: one from the bar because the bar is rigid, and another from the spring. What you need to ask yourself is, what are some limits I can take, what do I expect from the limits, and what do the limits from your equations actually give? For example, in the case that mass 2 is much bigger than mass 1, what physical system do you now have, and do your equations support it?

Not sure what you mean by "one from the bar", do you mean an angle that the center of the bar makes with the X axis? I hope so lol.

When m2>>m1... don't know what I'd have, I think my equation of motion is general enough. I guess you could say if one mass was really big, the bar wouldn't rotate much... maybe something worth studying from the point of small oscillations, but that's not what I'm asked in this problem. :P