Two-dimensional potential flow expressed by means of the complex potential function uses Euler coordinates, i.e. a fixed point approach. However, there are many cases where the identical particle time is required, for example the settling time of suspended particles, heat convection (because in incompressible potential flow the heat and flow equations are uncoupled), and dispersion of fluid particles due to distortion.

In real variables the differential equation for the Lagrange time is generally too complicated because it involves two coordinates as functions of time. In the following a differential equation of single complex variable is derived.