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**Double Atwood Machine: relation between the contraints & the variables ?!!**

Hello. I am taking an analytical mechanics course & there's 2 "simple" equations relating the constraints to the variables. The problem is actually a class example. Here is it

1. The figure of the example is attached.

We are supposed to find the Lagrangian L = T-V, but I was stuck at correctly proving the following (for which I am asking for help in proving). I should note that I was able to find L & the equations of motion by altering the figure & making use of the height of the masses relative to (my) chosen reference.:

(x

_{2}+ x

_{1}) - l =0 && (2x

_{1}+ x

_{2}+ x

_{3}) - (2l + l') =0

2. NO Relevant equations: simple arithmetic

3. The Attempt at a Solution :

Apparently l = x

_{p}+ x (though another element should be added -- can you tell me why this cannot be added ? -- & that is: [tex]\pi[/tex] a, where a is the radius of the pulley).

Moreover,

x

_{3}= (l' - x') + x

_{p}= (l + l') - (x

_{1}+ x')

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