"Hey Rockie, watch me pull a rabbit out of my hat...oops wrong hat". :-)
If the simultaneous differential equations approach didn't fly well, how about using "fourier transformations?". Since no one has mentioned it yet.
I had a teacher once who claimed you could use fourier analysis to get an "equation of your handwritten signature".
He never demonstrated it, but it would seem that it would be
done from taking datapoints of the signature.
I just did a groups.google.com search for
"fourier equation from data points" and it seems to be a well discussed problem. One of the solutions said to use "Legendre polynomials."
I'm not really a human, but I play one on earth.
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