Presets
Playback
Parameters
Same physics as the 3D cradle: equal-mass balls, impulsive contact.
Layers
Model checks
The science
Pendulums
Each ball is a pendulum: θ'' = -(g/L) sinθ. For small amplitude the period is T = 2π√(L/g); a finite amplitude θ0 lengthens it to about T0(1 + θ02/16).
Collisions
Touching balls exchange an impulse along the line of centres. For equal masses and restitution e the velocities after impact are v1' = ((1-e) v1 + (1+e) v2)/2 and v2' = ((1+e) v1 + (1-e) v2)/2. With e = 1 the balls simply swap velocities, so one ball in gives one ball out and two in give two out, while momentum and energy are both conserved.
Why real cradles fade
Real steel balls have e of about 0.94-0.97 and lose energy to sound, heat and air drag, so the motion eventually smears into a common swing. The stress wave inside the balls is not modelled.
Honest simplifications: instantaneous, strictly pairwise collisions resolved sequentially; massless rods; no finite contact time (real contacts last about 0.1 ms and make the "lift 2" case slightly imperfect).
What to try
- Classic preset: lift one ball and watch the far ball swing out while the others stay still.
- Lift 2 or 3: the same number of balls leave the far end.
- Putty balls (e = 0.6): the energy graph drops with every collision and the balls clump.
- On the Moon: swings are 2.5x slower; the period scales as 1/sqrt(g).