The Physics of Bounce
Every bouncing character, swaying chain, and wobbly jelly in a video game is powered by Hooke's Law: F = -kx. Springs are the most fundamental building block of animation physics because they produce natural-looking oscillatory motion with just two parameters — stiffness and damping. Chain multiple springs together and you get ropes, hair, and soft bodies.
Why Verlet Beats Euler
The naive approach to simulating physics — Euler integration — accumulates energy errors that cause springs to explode. Verlet integration, published by Luc Verlet in 1967 for molecular dynamics, computes the next position directly from the current and previous positions. This symplectic property conserves energy over long simulations, making it the backbone of physics engines from Hitman to Tomb Raider.
Damping and Energy Dissipation
Real springs lose energy to friction and air resistance. In simulation, damping is modeled by multiplying velocity by a factor slightly less than 1 each frame. The damping coefficient controls how quickly oscillations decay: low damping gives bouncy, playful motion; high damping gives heavy, sluggish movement. Finding the right damping is often the difference between animation that feels alive and animation that feels dead.
From Single Springs to Complex Systems
A single spring-mass pair oscillates predictably. But connect dozens of springs in grids, chains, or meshes and complex emergent behavior appears — waves propagate, nodes resonate, and the system develops a personality of its own. This is how cloth, jelly, and soft-body simulations work: simple local rules producing globally convincing deformation.