Recall for a particle with kinetic energy K = 1/2mx², the momentum is defined as

p = mx = dK/dx

Therefore, for a mechanical system with generalized coordinates q₁, ..., qₙ, we define the generalized momentum pₖ as

pₖ = ∂L/∂qₖ

where L is the Lagrangian of the system. With K = 1/2qᵀ D(q)q and L = K - V prove that

∑ⁿₖ₌₁ qₖpₖ = 2K