  The isomonodromic deformations underlying the Painlev\'e transcendants are
interpreted as nonautonomous Hamiltonian systems in the dual $\gR^*$ of a loop
algebra $\tilde\grg$ in the classical $R$-matrix framework. It is shown how
canonical coordinates on symplectic vector spaces of dimensions four or six
parametrize certain rational coadjoint orbits in $\gR^*$ via a moment map
embedding. The Hamiltonians underlying the Painlev\'e transcendants are
obtained by pulling back elements of the ring of spectral invariants. These are
shown to determine simple Hamiltonian systems within the underlying symplectic
vector space.
