FA-86919 / Physics integrator stability / Member archive

Underdamped eigenvalues use twice the imaginary part · case 04

Oscillatory systems report too much amplification and are flagged unstable early.

Member previewVariant 4 · 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 0	`["stable", 0.970887]`	`["stable", 0.963696]`	Failed

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