Consolidation of Lagrangian functionals for mathematical modelling of dissipative systems

The author highlights some of the features of a comprehensive effort, currently in progress, to construct a framework which allows formulation of variation principles for dissipative systems (linear and nonlinear). The main idea is to extend the conventional scope of variational calculus by allowing Lagrangians to include path-dependent integrals as variables. The appropriate generalized Lagrangian equations are formulated by fusing previous results of the author. This allows elimination of the time running backward from dynamical equations. Another limitation of previous results is also eliminated by taking nonzero initial (boundary) conditions into account. Finally, a variational principle for the Volterra integral equation is found within the framework of Lagrangian functionals.