DAlembertian Functions in Celestial Mechanics

K. V. Kholshevnikov

Astronomical Institute, St. Petersburg State University, St. Petersburg, Russia

Received January 12, 1996

Abstract—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’Ale-
mbertian 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.

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