Vector expression of precession and the checking of precession model

Given that the traditional method for expressing precession is based on spherical trigonometry, its defect lies in the arbitrary nature in determining the positive or negative signs of the spherical angles and sides of spherical triangles when determining them, as well as the difficulty in determining the theoretical relationships between different precession angles, and it is not conducive to the theoretical derivation of both the precession-nutation matrix and other theoretical aspects. To address this issue, this paper uses the inner product and outer product of two vectors to jointly define an angle (the angle and side length of a spherical triangle), such that the angle thus determined is unique, thereby avoiding the ambiguity in determining the positive or negative signs of angles using the spherical trigonometry method. By means of the representation of a specific vector in different coordinate systems and the transformation between different coordinate systems, the theoretical relationships between different precession angles can be directly obtained. Meanwhile, this study provides the polynomial expansions of precession angles and their trigonometric functions, thereby establishing a complete precession model involving all precession angles.This study points out that, on the order of tens of microarcseconds, the different precession angles in the IAU2006 precession model or the P03 precession model are not mutually consistent, necessitating a re-examination of the numerical computation of different precession angles. The research methods and results can be applied to research in fields such as the astronomical geodetic datum and data processing of space geodetic technology.