How can I model a double pendulum in op-amps?
Part of the problem of the double pendulum is that the behaviour is non-linear except at the limit of very small excursions. It follows that you need non-linear elements in your analog computer. For the double pendulum, the non-linear elements are sin/cosine calculators. You can implement the sinusoid elements with multiplier chips and a Taylor expansion, or with ADC/DAC converters and a ROM block.  If you calculate an equivalent expansion using exponentials instead of a power series, you can use diodes instead of multiplier chips.