FA-87324 / Physics integrator stability / Member archive

Zero initial energy is scaled by a tiny epsilon · case 04

A system starting at rest reports astronomically large drift for any motion.

Member previewVariant 4 · 3 implementations · 8 checks per implementation

Case contract

solve(states, k, m, tol, blowup): states [[x,v],...] of a spring integrator; E=0.5 m v^2+0.5 k x^2. Relative drift r=|E-E0|/E0 (absolute when E0=0). Scan in order: first state with E>blowup*E0 (E0>0) returns ["blowup", index, its r]. Otherwise ["drift", first index with r>tol, max r] or ["ok", -1, max r].

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 4	`["drift", 1, 2684793375.0]`	`["ok", -1, 0.002685]`	Failed

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