2D Chain & Rope — Verlet Dynamics (2D): Understanding the Physics of Flexible Structures

What is Verlet Integration?

Verlet integration is a numerical method used to solve Newton's equations of motion. It calculates the position of particles at each time step based on their previous positions and velocities, making it ideal for simulating flexible structures like chains and ropes.

This method avoids the need for complex force calculations at every step, providing a more efficient way to model dynamic systems.

How Does Stiffness Affect the Chain?

Stiffness in the chain represents how much it resists deformation. Higher stiffness means the chain will maintain its shape better under tension or compression.

Adjusting the stiffness slider allows you to observe how the chain's behavior changes, from a limp rope to a rigid structure.

The Role of Gravity and Damping

Gravity acts on each bead in the chain, pulling it downward. The gravity slider lets you control this force, allowing you to see how different gravitational strengths affect the chain's shape.

Damping represents energy dissipation due to friction or other dissipative forces. Increasing damping causes the chain to settle more quickly and with less oscillation.

Catenary Curves and Wave Propagation

When both ends of the chain are pinned, it forms a catenary curve, which is the shape that a hanging flexible cable or chain assumes under its own weight when supported only at its ends.

Pulsing one end of the chain can create wave-like disturbances that propagate along the rope, demonstrating how energy travels through the structure.

Frequently asked questions

Try it live

Everything above runs in your browser — open 2D Chain & Rope — Verlet Dynamics (2D) and change the parameters while it is running. Nothing is installed, nothing is uploaded, the whole model lives in one tab.