  A universal symplectic structure for a Newtonian system including
nonconservative cases can be constructed in the framework of Birkhoffian
generalization of Hamiltonian mechanics. In this paper the symplectic geometry
structure of Birkhoffian system is discussed, then the symplecticity of
Birkhoffian phase flow is presented. Based on these properties we give a way to
construct symplectic schemes for Birkhoffian system by using the generating
function method.
