I am looking for a special function which solves the equation of motion of a cabin on a Ferris wheel.
The e.o.m. reads
$$ \ddot{\phi} + a \, \sin\phi + b \, \sin(\phi - \tau) = 0 $$
with
$$ a = gl^{-1}\Omega^{-2} $$
$$ b = Rl^{-1} $$
$$ \tau = \Omega t $$
$R$ is the radius of the wheel, $\Omega$ is its angular velocity. $l$ and $m$ are length and mass of the pendulum representing the cabin. $\tau$ is the dimensionless time, derivative is w.r.t. $\tau$.
Does anybody know an exact solution of this diff. eq. in terms of special functions?