How to Derive Lagrange's Equations for a Double Pendulum?

yukawa
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Lagrange equation of motion



(from Marion 7-7)

A double pendulum consists of two simpe pendula, with one pendulum suspended from the bob of the other. If the two pendula have equal lenghts and have bobs of equal mass and if both pendula are confirned to move in the same plane, find Lagrange's equation of motion for the system. Do not assume small angles.

Which generalized coordinates should it choose? And how to made use of the constrains?
 
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Make a picture. You can see that the 2 angles formed with the vertical are the 2 needed generalized coordinates.
 
but are these two angles independent of each other? (in fact, i don't know how to determine whether two coordinates are independent of each other or not)
 

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