  Extremal principles can generally be divided into two rather distinct
classes. There are, on the one hand side, formulations based on the Lagrangian
or Hamiltonian mechanics, respectively, dealing with time dependent problems,
but essentially resting on conservation of energy and thus being not applicable
to dissipative systems in a consistent way. On the other hand, there are
formulations based essentially on maximizing the dissipation, working
efficiently for the description of dissipative systems, but being not suitable
for including inertia effects. Many at-tempts can be found in the literature to
overcome this split into incompatible principles. How-ever, essentially all of
them possess an unnatural appearance. In this work, we suggest a solution to
this dilemma resting on an additional assumption based on the thermodynamic
driving forces involved. Applications to a simple dissipative structure and a
material with varying mass demonstrate the capability of the proposed approach.
