Perfectly centered break of a perfectly aligned pool ball rack

Abstraction: Numerical billiards break simulation using Hertz contact mechanics

Key points:

• Simulated in Mathematica using ODE model with Hertz contact force: F = 10^11 * (2-d)^(3/2) when d < 2
• Entire collision completes in first 0.2 ms; balls overlap by no more than 0.025% of radius
• Back corner balls (11 and 15) shoot out at more than half the original cue ball speed (5.60 units/sec from 10)
• Ball 5 (center of back row) moves at only ~2% of initial cue speed; kinetic energy is conserved (sum of squared speeds = 100)
• System is a "sonic vacuum" (Nesterenko's term): speed of sound vanishes because Hertzian effective spring constant is zero at contact, causing supersonic shocks instead of ordinary sound waves
• Result depends on force-law exponent; linear (Hooke) and higher-power "stiff" laws produce noticeably different break patterns

Connections: Mathematica · Physics Simulation · Numerical Methods · Contact Mechanics

Source: http://mathoverflow.net/questions/156263/perfectly-centered-break-of-a-perfectly-aligned-pool-ball-rack/156407#156407