Physlib.ClassicalMechanics.Pendulum.CoplanarDoublePendulum

The configuration space of a coplanar double pendulum describes all possible spatial positions of the system. For a pendulum consisting of two point masses $m_1$ and $m_2$ connected by strings of length $l_1$ and $l_2$ to a fixed pivot, the configuration is uniquely determined by the two angles $\phi_1$ and $\phi_2$ that the strings make with the vertical axis. Mathematically, this configuration space is the 2-torus $T^2 = S^1 \times S^1$, where each $S^1$ represents the range of possible values for each angle $\phi_i \in [0, 2\pi)$.