Suppose a Hamiltonian system admits local action-angle coordinates $(I,\theta)\in A\times \mathbb T^n$, with $A\subset\mathbb R^n$ open, and suppose that in these coordinates the Hamiltonian has the form $H=H(I)$. Then Hamilton's equations are \begin{align*} \dot I =0 \end{align*} and \begin{align*} \dot\theta =\nabla_I H(I). \end{align*} Thus the motion is linear on invariant tori.