“…The standard time-dependent Ginzburg-Landau theory (TDGL), which contains the assumption of local equilibrium, and is formulated in the laboratory frame, is a powerful tool to study phenomena in the vicinity of the superconducting-normal phase transition. To study gyroscopes [1], gravitational wave antennae [2] and the interaction of the superconducting condensate with strong sound waves [3,4,5,6,7,8,9,10,11,12,13], where the atomic lattice is in motion, an extension to TDGL is needed to accommodate the dynamical system.…”