FA-86902 / Physics integrator stability / Member archive

Pendulum kinetic energy uses one power of the rod length · case 02

Energy diagnostics disagree with the integrated state for any rod length other than one.

Member previewVariant 2 · 3 implementations · 8 checks per implementation

Case contract

solve(theta_deg, omega, g, L, dt, steps): planar pendulum theta''=-(g/L)*sin(theta), initial angle in degrees, omega in rad/s, integrated with velocity Verlet carrying the acceleration between steps. Return [angle in degrees, omega, energy per unit mass 0.5*L^2*omega^2 + g*L*(1-cos theta)], 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	`[87.317304, -0.06935, 7.675568]`	`[87.317304, -0.06935, 7.681666]`	Failed

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

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