EXTENDED SCHUBART AVERAGING

The purpose of this paper is the presentation of an integrator for the average motion of an asteroid in mean motion commensurability with Jupiter. The program is valid for any (p + q)/p mean motion commensurability (except when q = 0) and uses a double precision version of DE (Shampine and Gordon 1975) as propagator. The averaged equations of motion of the asteroid are evaluated in a non-singular way for any value of the eccentricities and the inclinations and the orbit of Jupiter is described by the most important terms in Longstop 1B (Nobili et al. 1989). This integrator can be considered as an extension of the well known Schubart Averaging (Schubart 1978) in which Jupiter is moving on a fixed ellipse.