The Arm's Equations of Motion

The viewer can (1) derive ∂L/∂q̇ = Mq̇ (and say where symmetry is used), (2) differentiate Mq̇ in time with the product rule and Ṁ = Σ(∂M/∂qₖ)q̇ₖ, (3) compute ∂L/∂q componentwise as ½q̇ᵀ(∂M/∂qₖ)q̇, (4) assemble Mq̈ + Ṁq̇ − ∂/∂q(½q̇ᵀMq̇) = 0 and write both rows for the two-link arm, (5) explain the conserved shoulder momentum.