The cradle is a chain of equal steel pendulums hung so that the balls just touch. Each ball obeys θ'' = -(g/L) sin θ - c θ' (swing plus air drag). Contacts are resolved as instantaneous impulses along the line of centres: for equal masses j = (1+e)(v₁-v₂)/2, so with e = 1 the velocities swap, which is why one ball in sends exactly one ball out. Several simultaneous contacts are resolved by repeated sweeps along the chain.

Momentum and kinetic energy are both conserved for e = 1; with e < 1 a little energy is lost at every collision and the balls blur into a rigid-looking slug, as with real "dead" balls. The period of a large swing exceeds the small-angle value 2π√(L/g): the exact result is T = 4√(L/g)·K(sin(θ₀/2)).

Simplifications: perfectly rigid, point-contact balls with a single restitution coefficient (real cradles also lose energy to sound and wave propagation inside the balls), strings are massless and inextensible, motion stays in one plane. The "String length" slider is in decimetres.