  The 3.5 post-Newtonian (PN) order is tackled by extending the canonical
formalism of Arnowitt, Deser, and Misner to spinning objects. This extension is
constructed order by order in the PN setting by utilizing the global Poincare
invariance as the important consistency condition. The formalism is valid to
linear order in the single spin variables. Agreement with a recent action
approach is found. A general formula for the interaction Hamiltonian between
matter and transverse-traceless part of the metric at 3.5PN is derived. The
wave equation resulting from this Hamiltonian is considered in the case of the
constructed formalism for spinning objects. Agreement with the Einstein
equations is found in this case. The energy flux at the spin-orbit level is
computed.
