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kinetic energy in Lagrangian

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Please see the attached file.

I need an explanation of how one gets from the top equation (with v)s given by to the bottom equation where v is given by l*(theta)dot. I do not need an explanation of the double pendulum.

Derive the kinetic energy equation of the double pendulum in Lagrangian.

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It shows the steps of deriving the given kinetic energy equation in Lagrangian for the double pendulum.

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