Differential Equations, Analog Computing, and Emacs Updates (publ. 2025-07-14)

My apologies for the long delay since my last post: as far as outdoor activities, there was a combination of personal and work distractions, along with weather issues — such as forest fire smoke — that made it difficult for several weeks to get out for my usually summer lunchbreak walks. I spend some of those lunchbreaks hacking Emacs Calc, trying to implement a feature that I requested as a wishlist item. I haven't made much concrete progress on that, however, so I won't discuss it further at the present time.

Last week I was distracted by an arduous ordeal involving muscle spams, brought on by an accidental blunt force impact to my back. It was a less than pleasant experience overall. But I was glad that, during the experience, I was able to continue trusting the LORD and not get angry, bitter, or despondent, despite several days of intense pain. Faith is the victory, as the old hymn says!

During that time, I could not work on anything that I normally work on, as it was very painful to sit, to stand, or to bend over a bench or a keyboard. I was, however, able to spend some quality time inside a differential equations textbook which someone gave me a while back. I only made it through about two chapters, but even that was helpful in clarifying and refining my understanding of a few DE and modeling concepts. I also learned some interesting things about modeling cable tension and sag, which might prove handy if I ever need to design a suspension bridge.

This last month, I had tried to implement a few advanced models, in particular the Lorentz attractor, on my home-made analog computer, but was frustrated by not getting the expected results. So I started looking into what on the system might need tuning or might be broken. One thing I did notice is that one of the voltage reference ports — I can't remember which one it was originally — was off target by around 500 mV. The two ports are supposed to be +10V and -10V. I realized I couldn't fix the problem, however, as the one tuning potentiometer in the design of the reference voltage effects the gain of both outputs equally. So I had to redesign the module slightly to insert an additional potentiometer which could adjust the gain of just one of the ports — the +10V port, in fact. This is practically the equivalent of a "zero offset" potentiometer, for setting the center point. After adjusting the gain of the +10V port to match that of the -10V port, I could then adjust the simultaneous gain potentiometer to bring both ports to within about 20 mV of the +/- 10V targets.

I am planning, God willing, to re-tune the offset on the integrators, as well as take a closer look at the behavior of the open amplifiers.

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