FA-87075 / Physics integrator stability / Member archive

Leapfrog starts without offsetting velocity by half a step · case 05

The orbit phase is shifted and energy oscillation is biased from the first step.

Member previewVariant 5 · 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	`[1.391453, -2.082042]`	`[1.380971, -2.155206]`	Failed

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

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