Featherstone's algorithm
An algorithm that computes the dynamics of a chain of jointed bodies in linear time — and is the reason some ragdolls' arms don't drift off their shoulders.
Roy Featherstone published the Articulated Body Algorithm in 1983, with robot arms in mind. The naive way to solve an articulated body builds and inverts a mass matrix, costing O(n³) in the number of joints; Featherstone gets the same answer in O(n) by sweeping out along the chain and back again. Bodies are described in reduced coordinates — joint angles rather than free positions — so joints cannot separate by construction.
Most game engines otherwise simulate ragdolls as free rigid bodies held together by constraints, which is cheap but stretches under load. PhysX articulations and Bullet's btMultiBody are built on Featherstone precisely to avoid that.