Hamilton’s equations $\dot q = \partial_p H, \dot p = -\partial_q H$ on the cotangent bundle, and their reduction by symmetry — including Lie–Poisson dynamics on $\mathfrak g^$ for a Lie group $G$. The SE(2) sub-Riemannian geodesic equations of the Geometry of Seeing series are exactly Lie–Poisson on $\mathfrak{se}(2)^$.