What is an elastic collision?

An elastic collision conserves both linear momentum and total kinetic energy — no energy is lost to heat, sound or deformation. Hard discs bouncing off each other in a sealed box approximate this ideal closely.

How does this 2D version differ from the 3D one?

Both drive the exact same impulse-based collision physics and the same Maxwell-Boltzmann statistics. This companion renders on a flat HTML5 canvas instead of a WebGL scene, and pairs the arena with a live histogram panel so the speed distribution and its theoretical curve are visible side by side rather than in a separate modal.

Why does the speed histogram converge to a curve?

Even though the initial velocities are randomised, repeated elastic collisions redistribute kinetic energy among particles until the system reaches thermal equilibrium. At equilibrium the speed distribution matches the Maxwell-Boltzmann curve f(v) = (m/kT)·v·exp(−mv²/2kT) for a 2D gas.

What happens when the mass ratio is not 1?

By the equipartition theorem, both particle types settle at the same mean kinetic energy, not the same mean speed. The lighter type ends up moving faster on average, which you can see directly by turning on velocity vectors.

Home▸Physics & Mechanics▸Elastic Collisions — 2D Billiards & Maxwell-Boltzmann (2D)

Elastic Collisions — 2D Billiards & Maxwell-Boltzmann (2D)

2D canvas companion: N frictionless discs colliding elastically, with a live speed histogram converging on the Maxwell-Boltzmann curve, momentum/energy readouts, and a mass-ratio slider to watch equipartition happen in real time.

Physics & Mechanics2DEasy60 FPS📱 Mobile-adapted⇄ 3D version

This 2D companion drives the same impulse-based elastic-collision physics as the 3D version through a plain canvas view: a side panel exposes particle count, disc radius, speed scale and the A:B mass ratio, a live readout tracks total kinetic energy, momentum and temperature, and a speed histogram redraws every frame beside the theoretical Maxwell-Boltzmann curve so you can watch a randomised initial state settle into thermal equilibrium without any 3D scene to orbit or load.

⚙ Under the hood

N frictionless discs bounce inside a box under perfectly elastic pairwise collisions computed from an impulse formula, conserving momentum and kinetic energy exactly. A live histogram panel compares the current speed distribution against the theoretical 2D Maxwell-Boltzmann curve as the system equilibrates.

elastic collisionbilliardskinetic theoryMaxwell-BoltzmannCanvas 2D

2D · HTML5 Canvas 2D · 60 FPS target · runs fully client-side, no install