I'm making a double pendulum for an art installation, and I would like to add energy to the system to compensate for friction and air drag losses so it can run more or less indefinitely.
The design so far has the top pendulum connecting to an axle at the top which is parallel to the ground and can rotate freely. So far I've sketched out a design which uses a rotational position sensor and a microcontroller to determine the pendulum shaft's current speed and position. A small, reversible electric motor will connect to the axle with a somewhat "limp" drive belt around the consistency of a rubber band (to lessen the impact of rapid chaotic changes mismatching with power input direction). As the axle rotates unpredictably, the control software will reverse or advance the motor to add a slight force in the current direction of rotation. Once tuned, the hope is that it will not perceptibly interfere with the natural motion of the pendulum while adding enough energy to keep the pendulum swinging with the same total energy as it started at.
Questions: 1) Are there mechanically simpler ways of adding energy to such a chaotic system? 2) Will energy added to the top pendulum distribute to the bottom pendulum in a way that would leave a casual observer unaware, or would the system develop obviously unnatural motion? 3) How can I roughly estimate (+-50%, to size the drive motor) the average energy input required to overcome friction and drag losses?