Euler-Lagrange Equation

The fundamental equation of Lagrangian mechanics: d/dt(∂L/∂q̇) - ∂L/∂q = Q, where L = T - V is the Lagrangian and Q is the generalized force. Applying the Euler-Lagrange equation to a robot's kinetic and potential energy yields the manipulator equation of motion M(q)q̈ + C(q,q̇)q̇ + g(q) = τ.