Let me preface this by saying that I'm not an expert, nor do I conclusively understand how op-amps work, but I have a strong suspicion that this should be possible, at least crudely.
I have this idea that by using op-amps to measure the voltage difference across the terminals of a DC motor, amplify that difference, then take the integral of that voltage with respect to time, I could represent the net rotation of the motor as a voltage on an output pin, eg. 2.5 V @ 0 turns, 3.0 V @ 1 turn CW, 2.0 V @ 1 turn CCW, etc.
The voltage across a motor's terminals is proportional to its speed, so in theory (in math) I should be able to integrate and get position. However, I would also need to know how an op-amp works well enough to be able to implement it. In my defense, I really thought I did.
Is this even possible? I'm not very concerned about it being practical (I am a mathematician at heart, I'm on the wrong side of stack exchange here), I just want to know if these principles do, in fact, work this way.
Is an op-amp even the right component to use? If comparing, amplifying, and integration is the way I'm going about this, are there different chips I can use instead? I am aware of the broader strokes and concepts, that op-amps compare voltages, multiply, take differences, do integrals, etc. but the finer details of use and implementation are very much so lost on me.
Does anyone have any links to resources to better get a handle on this kind of stuff? I find electronics absolutely fascinating, but it seems to have a very high barrier to entry. Any piece I read about using op-amps is either super dense with an expected background or so vague that it may as well be talking about Alchemy. I took AP Physics in high school, and we had an electricity chapter, so that's a good foundation for first principles, but there are second principles, third principles, fourth, fifth, etc. that I am in desperate need of. I would really love to be able to try out things like this and learn firsthand the difficulties of implementation. Ultimately, that will make any further ideas better conceived and executed.
If, by a long shot, this circuit is possible and practical, please try it yourself. I would love to hear others' opinions on the functionality of such analog devices and how to make them better.