A new precession formula

We adapt J. G. Williams' expression of the precession and nutation using the 3-1-3-1 rotation to an arbitrary inertial frame of reference. The modified formulation avoids a singularity caused by finite pole offsets near the epoch. By adopting the planetary precession formula numerically determined from DE405 and by using a recent theory of the forced nutation of the nonrigid Earth by Shirai & Fukishima, we analyze the celestial pole offsets observed by VLBI for 1979 - 2000 and determine the best-fit polynomials of the lunisolar precession angles. We then translate the results into classical precession quantities and evaluate the difference due to the difference in the ecliptic definition. The combination of these formulae and the periodic part of the Shirai-Fukishima nutation theory serves as a good approximation of the precession-nutation matrix in the International Celestial Reference Frame. As a by-product, we determine the mean celestial pole offset at J2000.0 as (X) over bar (0) = -(17.12 +/- 0.01) mas and (Y) over bar (0) = -(5.06 +/- 0.02) mas. Also, we estimate the speed of general precession in longitude at J2000.0 as p = 5028."7955 +/- 0."0003 per Julian century, the mean obliquity at J2000.0 in the inertial sense as (epsilon(0))(I) = 84381."40621 +/- 0."00001 and in the rotational sense as (epsilon(0))(R) = 84381."40955 +/- 0."00001, and the dynamical flattening of Earth as H-d = (3.2737804 +/- 0.0000003) x 10(-3). Furthermore, we establish a fast way to compute the precession-nutation matrix and provide a best-fit polynomial of an angle to specify the mean Celestial Ephemeris Origin.