Spontaneous parametric down-conversion like oscillations in a partially inverted double pendulum

Abstract We present the nonlinear motions of a partially inverted coplanar double pendulum with velocity-dependent damping under parametric driving. It shows a new type of complex periodic and quasiperiodic oscillations where the sum of two dominating frequencies of the solution is equal to the driving frequency, which is analogous to the phenomenon of spontaneous parametric down-conversion (SPDC). The dominating response frequencies of the double pendulum are independent of the normal mode frequencies when such motion occurs.