The Lagrangian

The motion is derived from the system's Lagrangian ($L=T-V$), which describes its kinetic ($T$) and potential ($V$) energies.

$$ L = \frac{1}{2}(m_1+m_2)l_1^2\dot{\theta}_1^2 + \frac{1}{2}m_2l_2^2\dot{\theta}_2^2 + \dots $$