Math & Kinematics

Lagrangian Dynamics

Lagrangian dynamics is a formulation of classical mechanics that derives a system's equations of motion from the Lagrangian, defined as kinetic energy minus potential energy, via the Euler-Lagrange equations. For robot manipulators it yields the standard form M(q)q̈ + C(q, q̇)q̇ + g(q) = τ, relating joint torques to motion through the mass matrix, Coriolis terms, and gravity vector. It is often more systematic than Newton-Euler methods for deriving closed-form dynamics.

Why it matters for physical AI

Accurate dynamics models underpin torque control, gravity compensation, and physics simulators used to train policies, and they anchor system identification when transferring simulation-trained controllers onto real hardware.