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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 = TV, 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')
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 = TV, 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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