The lab
Rope Bridge Physics
A rope or chain hanging between two anchor points under gravity, simulated with Verlet integration. Drag anchors to move them, drag the rope itself to disturb it. Tension at each segment is visualized as a color gradient — blue for low, red for high.
xn+1 = 2xn − xn−1 + a·dt² · Verlet (1967) · position-based dynamics · catenary y = a·cosh(x/a)
running
drag anchors or rope · adjust physics below
low
high
presets
1.4
40
980
0
0.99
1.0
The catenary — the curve a hanging chain makes under its own weight — is not a parabola, despite Galileo’s guess. It’s a hyperbolic cosine: y = a·cosh(x/a), where a depends on the chain’s weight and tension at the lowest point. Leibniz, Huygens, and Johann Bernoulli solved it in 1691.
This simulation uses Verlet integration, the same method behind most physics engines’ rope and cloth simulations. Each point stores only its current and previous position — no explicit velocity. Constraints (fixed segment lengths) are enforced iteratively after each time step.
Try dragging an anchor point high, then release. Watch the catenary oscillate and settle. The "Wind buffeting" preset applies a sinusoidal lateral force.
Related: Catenary curves · Verlet physics · Cloth simulation