Phase variables in analytical celestial mechanics are usually subdivided into positional and angular variables. The concept of the D’Alembertian function was used as long ago as 1977 to describe the behavior of the coordinates and Hamiltonians in planetary problems in celestial mechanics. This is an analytical function of a pair of action-angle variables possessing certain properties. In particular, the larger the range of values for the "action" variable, the narrower the range for the "angle" variable. This paper begins a short series of articles examining the basic functions of celestial mechanics from the point of view of whether they possess this D’Alembertian property. The results are applied to planetary and satellite motions. This first paper establishes the most important properties of D’Alembertian functions and determines the exact D’Alembertian radii for the "true anomaly minus eccentric anomaly" and "eccentric anomaly minus mean anomaly" differences.