I'm interested in chaotic circuits; and while many circuits that model attractors like Chua's Circuit, Lorenz Attractor, and RC phase shift networks are available, I would really like to model the behaviour of a double pendulum using op-amps.

I've seen a few references to the possibility of computing the differential equations describing the motion of a double pendulum; but no concrete implementations. How could I go about modeling this behaviour using op-amps?

  • \$\begingroup\$ Chua Chaotic cct tinyurl.com/y8lddwhb \$\endgroup\$ – Tony Stewart Sunnyskyguy EE75 Aug 1 '18 at 2:57
  • \$\begingroup\$ I'm aware of Chua's Circuit, as I stated in my question. The question is not how to generate ANY chaotic dynamical system, but specifically how to model a double pendulum. \$\endgroup\$ – sehrgut Aug 1 '18 at 4:31
  • \$\begingroup\$ This is a 50 yr old grad thesis topic of a double inverted pendulum easily found on web. You need some understanding of control theory. Do they still do this one? here's another Chaos circuit tinyurl.com/yap3x3rf \$\endgroup\$ – Tony Stewart Sunnyskyguy EE75 Aug 1 '18 at 4:52
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    \$\begingroup\$ Begin with the equation. Then decide how you will output a one dimensional signal (a voltage) that represents a one-dimensional value from the pendulum. Then come back and modify your question with this detail. \$\endgroup\$ – Andy aka Aug 1 '18 at 9:52
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    \$\begingroup\$ The fundamental Physics Model must be defined before it's realization in Analog Electronics. Learn to articulate the characteristics to make this question worthy of an answer. \$\endgroup\$ – Tony Stewart Sunnyskyguy EE75 Apr 21 '19 at 16:34

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.


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