Well any nonlinear model using atan2 function would be realistic.
For example calculating aerodynamic forces of an aircraft one have to know angle of attack and sideslip angle which is usually calculated as atan2 on 2 of velocity components.
More on history importance uses and motivation behind existence of atan2 function one can find on wikipedia page.
That function available in all math libraries for all languages I know starting from C. It is supported by most nonlinear optimisation tools like CasADi for example.
It is unfortunate that Julia decided to implement atan2 as one more method for atan function. Combining unary and binary versions under the same name. Which causes confusions in packages like JuMP since then…