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PolskiSnowball Hill: Accretion-Coupled Rolling Growth (2D)
2D rolling-accretion lab: a real dm/dt-coupled ODE system — snow pickup, growing moment of inertia, variable-mass rolling dynamics — drives a snowball's radius, mass and speed down a slope, with a live r∝√s growth-curve check against the analytic solution.
This 2D companion drives the same rolling-snowball idea as the 3D scene through real accretion physics instead of a scripted size-up animation: the ball's volume growth is derived from the actual swept-strip geometry (dV = k·2r·h·ds), giving a closed-form r(s) = √(r₀² + (kh/π)s) growth law that the live plot checks itself against every frame, and the ball's speed follows a genuine variable-mass rolling equation of motion — energy conservation for a solid sphere (I = 2/5·mr²) coupled to the momentum cost of absorbing stationary snow — so slope, snow depth, snow density, initial size, stickiness and rolling friction all measurably change the growth-vs-distance curve and the final radius and speed.
Rolling-accretion lab with a real dm/dt-coupled ODE system — snow pickup, growing moment of inertia, variable-mass rolling dynamics — and a live r∝√s growth-curve check against the closed-form analytic solution.
2D · HTML5 Canvas 2D · 60 FPS target · runs fully client-side, no install