Open Dynamics Engine (ODE)

Russell Smith released ODE in 2001, at a time when serious game physics otherwise meant an expensive Havok licence. The library simulates rigid bodies connected by joints — hinges, ball-and-socket, sliders — and ships its own collision detection. Joints with friction and motors made it a natural fit for vehicles and, yes, ragdolls.

Games moved on to Bullet and PhysX, but robotics stayed: the Gazebo simulator used ODE as its default physics engine for many years. The C API is old and development is slow, which in this case mostly means the same simulation gives the same answer it did fifteen years ago.