Lagrangian of falling disk connected to another disk

[Elvis 123456789]

Homework Statement

String is wrapped around two identical disks of mass m and radius R. One disk is fixed to the ceiling but is free to rotate. The other is free to fall, unwinding the string as it falls. Find the acceleration of the falling disk by finding the lagrangian and lagrange's equation of motion.

Homework Equations

L = T - V

L = ∂L/∂x - d/dt(∂L/∂x-dot) = 0

The Attempt at a Solution

my attempt at the solution is in the attachment. I feel uneasy with my choice for the constraint equation. Can anybody take a look and tell me if it looks ok?

 

[TSny]

Your solution looks correct.

Posting a picture of a handwritten solution is inconvenient for the homework helper because it makes it difficult to "quote" a particular part of the solution. It would have been helpful to show more steps in arriving at the green formula for L, but it looks right. There is a glare spot on the picture that hides some of your work.

I point these things out because these are things that might make a homework helper less willing to wade through your work.

But, that aside, your solution looks good!

 

[Elvis 123456789]

Your solution looks correct.

Posting a picture of a handwritten solution is inconvenient for the homework helper because it makes it difficult to "quote" a particular part of the solution. It would have been helpful to show more steps in arriving at the green formula for L, but it looks right. There is a glare spot on the picture that hides some of your work.

I point these things out because these are things that might make a homework helper less willing to wade through your work.

But, that aside, your solution looks good!

Thank you for taking the time to respond. I often take pictures of my work because typing it out often looks really messy and weird and so I figured it would actually help the homework helpers see my work better; but I see your point. Thanks for the feedback.