FA-87142 / Physics integrator stability / Member archive

Current and previous step lengths are swapped · case 02

Accelerating or decelerating frame rates distort the trajectory in opposite directions.

Member previewVariant 2 · 3 implementations · 8 checks per implementation

Case contract

solve(x0, v0, w2, g, dts): position Verlet with variable steps, acceleration -w2*x+g. First step is Taylor x1=x0+v0*h0+0.5*a(x0)*h0^2; then x_{n+1}=x_n+(x_n-x_{n-1})*(h_n/h_{n-1})+a(x_n)*h_n*(h_n+h_{n-1})/2. Velocity estimate is (x_n-x_{n-1})/h_last. Empty dts returns the initial state. Return [x, v] rounded.

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	`[1.902154, 0.528281]`	`[1.910483, 0.457456]`	Failed

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

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