Position-based dynamics
A physics method that solves constraints by nudging positions directly instead of integrating forces, trading physical accuracy for rock-solid stability.
Introduced by Müller and colleagues at NVIDIA in 2006. Rather than computing forces, acceleration and velocity, PBD projects the particles' positions until the constraints — distance, volume, angle — are satisfied, then derives the velocity from the position change. The result is fast, controllable and rarely explodes.
That is why the method drives cloth, ragdolls, soft bodies and fluids in a great many games. Its weakness is that perceived stiffness depends on the iteration count; XPBD (2016) fixes this by introducing a properly unit-ed, regularised constraint. Verlet integration is the simpler relative in the same family.