  It is shown that one can obtain canonically-defined dynamical equations for
non-conservative mechanical systems by starting with a first variation
functional, instead of an action functional, and finding their zeroes. The
kernel of the first variation functional, as an integral functional, is a
1-form on the manifold of kinematical states, which then represents the
dynamical state of the system. If the 1-form is exact then the first variation
functional is associated with the first variation of an action functional in
the usual manner. The dynamical equations then follow from the vanishing of the
dual of the Spencer operator that acts on the dynamical state. This operator,
in turn, relates to the integrability of the kinematical states. The method is
applied to the modeling of damped oscillators.
