FA-87295 / Physics integrator stability / Member archive

Mean period divides the span by the crossing count · case 05

The period is underestimated by a factor (n-1)/n.

Member previewVariant 5 · 3 implementations · 8 checks per implementation

Case contract

solve(xs, dt, omega): integrator frequency diagnostic. Upward crossings are samples with x[i-1]<0<=x[i], timed by linear interpolation. Period is the mean interval (last-first)/(count-1); relative error vs 2*pi/omega. Fewer than two crossings gives [None, count, None]. Return [period, count, error] rounded to 6.

Why this case matters

Game and robotics physics loops depend on integrator update order, step control and stabilization terms; a wrong decision point turns a stable simulation into drifting or exploding motion.

One recorded failure

Sample boundary fixture

This sample comes from the broken implementation of a controlled reproducer.

Boundary fixture	Actual	Expected	Outcome
case 0	`[0.674052, 4, -0.505338]`	`[0.898735, 4, -0.340451]`	Failed

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