Math & Kinematics

Rigid Body Dynamics

Rigid body dynamics is the study of forces and motion for systems of interconnected rigid links, expressed for manipulators by the equation M(q)q̈ + C(q, q̇)q̇ + g(q) = τ relating joint torques to accelerations. Efficient recursive algorithms, including the recursive Newton-Euler and Featherstone's articulated-body algorithm, evaluate inverse and forward dynamics in linear time and power both physics engines and model-based controllers, with libraries such as Pinocchio providing optimized implementations.

Why it matters for physical AI

Dynamics models are the shared foundation of simulation, model predictive control, and system identification, and their fidelity limits everything built above them, from sim-to-real transfer to whole-body torque control.