Integrability of flows in phase space

dynamical system, global integrability of a dynamical system, and integrability of a set of velocities defined by a transformation on a set of time derivatives of holonomic coordinates (‘generalized velocities’). In the latter case, the time integrals of the transformed velocities yield either a set of holonomic coordinates or a set of nonholonomic coordinates, depending on whether the infinitesimal transformation is integrable. We show how a dynamically simple set of holonomic coordinates in phase space is generated whenever the local integrability of a dynamical system leads to global integrability.