This article is the second of a pair of articles about the Goldman symplectic
form on the PGL(V )-Hitchin component. We show that any ideal triangulation on
a closed connected surface of genus at least 2, and any compatible bridge
system determine a symplectic trivialization of the tangent bundle to the
Hitchin component. Using this, we prove that a large class of flows defined in
the companion paper [SWZ17] are Hamiltonian. We also construct an explicit
collection of Hamiltonian vector fields on the Hitchin component that give a
symplectic basis at every point. These are used to show that the global
coordinate system on the Hitchin component defined iin the companion paper is a
global Darboux coordinate system.Comment: 95 pages, 24 figures, Citations update