Physical Principles & Mathematical Derivation
Vector momentum conservation combined with scalar kinetic energy conservation proves geometrically that any non-head-on elastic collision between an incoming sphere and an identical stationary target deflects the pair at a right angle (p⃗₁′ · p⃗₂′ = 0) — fundamental from pool tables to Rutherford particle physics!
Questions & Concepts
What physical equation governs 2D Glancing Billiard Scattering & 90° Orthogonal Split Simulator?
p⃗₁ + p⃗₂ = p⃗₁′ + p⃗₂′ (m₁=m₂, v₂=0, e=1 ⇒ θ₁ + θ₂ = 90°) — Vector momentum conservation combined with scalar kinetic energy conservation proves geometrically that any non-head-on elastic collision between an incoming sphere and an identical stationary target deflects the pair at a right angle (p⃗₁′ · p⃗₂′ = 0) — fundamental from pool tables to Rutherford particle physics!
How are the equations of motion integrated in this simulation?
Nonlinear differential equations are integrated at 240–300 Hz substeps using classical 4th-order Runge-Kutta (RK4) to maintain strict Hamiltonian energy accuracy.