  It is shown that physical mechanics for pointlike bodies can be effectively
modeled in terms of the action of transformation groups that act as symmetries
of the solutions of systems of differential equations that describe the
integrability of dynamical states. The equations of motion are then obtained
from these integrability equations for the dynamical states. It is also
observed that the functions that define the components of a dynamical state
represent a set of mechanical constitutive laws. The variational formulation of
mechanics is shown to be a specialization of these principles.
