FA-87157 / Physics integrator stability / Member archive

Quaternion derivative omits the one-half factor · case 02

Bodies spin at twice the commanded angular velocity.

Member previewVariant 2 · 3 implementations · 8 checks per implementation

Case contract

solve(q, omega, dt, steps): orientation quaternion [w,x,y,z], world-frame angular velocity omega. Each step q += 0.5*dt*(0,omega) (x) q (Hamilton product, omega on the left), then renormalize to unit length. Return q with w>=0 (negate all components otherwise), 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	`[0.027424, 0.725586, -0.677112, -0.119549]`	`[0.000571, 0.704341, -0.687306, -0.177522]`	Failed

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This record includes three runnable implementations, regression fixtures, execution results, and source hashes.

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