Generalized variational principle in dissipative hydrodynamics and continuum mechanics

A formulation of the generalized variational principle for dissipative hydrodynamics and continuum mechanics is presented as a sum of the Hamilton and Onsager variational principles in terms of displacement of mechanical and heat fields. In this case, the dissipative hydrodynamic system corresponds to the motion equations of mechanical and heat fields derived from the extreme condition for action with a Lagrangian density in the form of the difference between the kinetic energy and the free energy minus the time integral of the dissipation function with quadratic forms of all terms.