  We present a multi-scale modeling and simulation framework for low-Reynolds
number hydrodynamics of shape-changing immersed objects, e.g., biological
microswimmers and active surfaces. The key idea is to consider principal shape
changes as generalized coordinates, and define conjugate generalized
hydrodynamic friction forces. Conveniently, the corresponding generalized
friction coefficients can be pre-computed and subsequently re-used to solve
dynamic equations of motion fast. This framework extends Lagrangian mechanics
of dissipative systems to active surfaces and active microswimmers, whose shape
dynamics is driven by internal forces. As an application case, we predict
in-phase and anti-phase synchronization in pairs of cilia for an experimentally
measured cilia beat pattern.
