  We study the time evolution of a sessile liquid droplet, which is initially
put onto a solid surface in a non-equilibrium configuration and then evolves
towards its equilibrium shape. We adapt here the standard approach to the
dynamics of mechanical dissipative systems, in which the driving force, i.e.
the gradient of the system's Lagrangian function, is balanced against the rate
of the dissipation function. In our case the driving force is the loss of the
droplet's free energy due to the increase of its base radius, while the
dissipation occurs due to viscous flows in the core of the droplet and due to
frictional processes in the vicinity of the advancing contact line, associated
with attachment of fluid particles to solid. Within this approach we derive
closed-form equations for the evolution of the droplet's base radius, and
specify several regimes at which different dissipation channels dominate. Our
analytical predictions compare very well with experimental data.
