Is this correct? (Lagrangian mechanics)

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Homework Statement


Find the Lagrangian and solve for the equations of motion. (see attached image)


Homework Equations


Euler-Lagrange's equation.


The Attempt at a Solution



I just wanted to check if I picked the right generalized coordinates. The pic shows what I think is called a Thompson-Tait pendulum. I chose the red dot as my reference frame and chose these as my generalized coordinates: the angles each of the pendulums at the ends make and phi as the angle at the center of pendulum.

I got a total of 3 holonomous constraints: z1, z2 = constant(all motion is planar), and (L + a)^2 = x^2 + y^2 for both pendulums at the ends.

Are my choices correct? Its a monster of a Lagrangian.
 

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