FA-86910 / Physics integrator stability / Member archive

Stability discriminant uses raw stiffness instead of k over m · case 05

Heavy bodies are classified with the eigenvalues of a unit-mass system.

Member previewVariant 5 · 3 implementations · 8 checks per implementation

Case contract

solve(k, m, c, dt): classify explicit Euler on x'=v, v'=(-k*x-c*v)/m. Eigenvalues are the roots of s^2+(c/m)s+k/m; amplification is max |1+dt*lambda|. Return ["marginal" if |amp-1|<=1e-9, else "stable" if amp<1, else "unstable", amp 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 1	`["unstable", 5.047531]`	`["unstable", 3.258936]`	Failed

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