Jhaunton In the case above this means the error rate goes from approx +0.23" per sec to -0.23" per sec virtually instantaneously - the peaks are sharp. Just a thought.
They are probably not instantaneous -- just appears so when the curve is shrunk on a finite graph.
The way to view it is to look at the periodic error curve as a Fourier Series. For good mounts, terms after the third harmonics are very small. For worse mounts, you may see large 5th, and even 7th harmonic terms.
In any case, each of these components of the Fourier Series is a continuous function -- and since they are sinusoidal, the sign change occurs when the magnitude of the first derivative of the curve is small. I.e., you don't go from +0.23" to -0.23", you go through +0.2...+0.10, ... +0.8,... +0.1, 0, -0.1, -0.2, ... etc. And the slopes near 0 are easy to guide away.
Mathematically, the second derivative (how fast the first derivative changes) is actually quite small. I.e., no sudden change in slope.
Chen
