A single pendulum is a clock. A double pendulum is not: it is a system with two degrees of freedom whose motion cannot be written in closed form, and which will cheerfully do things no amount of solving will predict. Pull it to one side and let go, twice, with the slightest difference, and watch the two runs diverge.
The equations of motion for a double pendulum are perfectly well behaved: two coupled second-order equations, energy conserved to within the integrator's error, and they are integrated here with a fourth-order Runge-Kutta step of a two-hundred-and-fortieth of a second.
What cannot be done is to predict them. Because the system is chaotic, two states that differ by an unimaginably small amount diverge exponentially, so the only honest description of the future is a number written to a hundred decimal places. The mathematics of chaos is not that the equations are complicated; it is that they are simple and the sensitivity is intrinsic.