FA-87077 / Physics integrator stability / Member archive

Leapfrog reports the half-step velocity as the current velocity · case 02

Velocity output is offset by half a step, corrupting energy and contact logic.

Member previewVariant 2 · 3 implementations · 8 checks per implementation

Case contract

solve(x0, v0, w2, g, dt, steps): acceleration -w2*x-g. The engine stores velocity at half steps: vh=v0+a(x0)*dt/2, then per step x+=vh*dt; vh+=a(x)*dt. Output synchronizes velocity back to the integer step: [x, vh-a(x)*dt/2] 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	`[-0.646031, 0.181833]`	`[-0.646031, -0.104617]`	Failed

MEMBER ARCHIVE

The complete case is available to members.

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

Member access is invitation-based. Sign in with your invited account to inspect the sources.