FA-86845 / Physics integrator stability / Member archive

Symplectic Euler substep drifts position with the pre-kick velocity · case 05

A stiff spring that should orbit with bounded energy gains amplitude every frame.

Member previewVariant 5 · 3 implementations · 8 checks per implementation

Case contract

solve(x0, v0, k, m, c, dt, steps): damped spring a=(-k*x-c*v)/m integrated with semi-implicit Euler (velocity first, then position with the new velocity). Each frame of length dt is split into ceil(dt/0.05) equal substeps (at least one). Return [x, v] rounded to 6 decimals after steps frames.

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 1	`[-0.046804, 1.255377]`	`[-0.030782, 0.966174]`	Failed

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

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