Restitution measured at the bottom of a discrete overlap returns more energy than went in

Fact

A fixed step overshoots a surface: the body is integrated past it and the collision is detected on the next step, at depth d. Reflecting the velocity measured there is wrong, because the body kept accelerating over that extra depth. A position-correction pass then lifts it back to the surface without removing the speed it gained falling into it, so every bounce adds about m * g * d of energy.

With a 1/120 s step and an impact at 900 px/s the depth is ~7 px and the gain is about 1.3% per bounce. A perfectly elastic ball climbs roughly 25% higher after twenty bounces.

The correction is to reflect the speed the body had at the surface, by discounting the gravity it picked up below it:

const gn = Math.abs(dot(gravity, normal));
const submerged = penetration / approachSpeed + dt;   // + dt: this step's gravity
const atSurface = Math.max(0, approachSpeed - gn * submerged);
restitutionBias = restitution * atSurface;

Why it matters

It looks like a restitution coefficient that is set too high, so it gets tuned down — which hides it for one scene and leaves the energy gain in place for every other. It is not a tuning error; the model is adding energy, and any closed system built on it slowly heats up.

Halving the timestep halves the gain rather than removing it, so the fix looks like it "nearly worked" and invites more of it.

How to apply

• Discount both terms: the time spent below the surface (d / v) and the gravity already integrated into the velocity this step (dt).
• Prefer erring dissipative. A ball that loses half a percent per bounce reads as a real ball; one that gains reads as broken.
• Assert it directly: drop a ball with restitution 1 and check that it never rises above the height it was released from, over enough bounces to integrate the error.