1. Improved Algorithm for the Construction of the Non-Rigid Earth Rotation Series V.V. Pashkevich Central (Pulkovo) Astronomical Observatory of Russian Academy of Science St.Petersburg Space Research Centre of Polish Academy of Sciences Warszawa 2006

2. Obtainment of exactly algorithm for the Construction of the Non-Rigid Earth Rotation Series, which expressed in the function of the three Euler angles. The aim of the research is:

3. Expressions for Euler angles:

4. Algorithm of Bretagnon et al. 1999 Rigid Earth angular velocity vector: The derivatives of Euler angles for Non-Rigid Earth rotation: Non-Rigid Earth angular velocity vector is obtained by:

5. 1 iteration For example: Iterations for solve of the Algorithm of Bretagnon et al. 1999

6. n iteration For example: Iterations for solve of the Algorithm of Bretagnon et al. 1999 Iterations is repeated while then absolute value of the difference between K-1 and K iterations is more than some DEFINITE values 

7. Cascade method: Common form for the periodic part of Euler angles:

8. Common form for the secular part of Euler angles:

9. A l g o r i t h m 2006

11. C o m m e n t NOTE that t=0 for the arguments in all expressions: Expressions (5), (6) and some expressions in the algorithm of Bretagnon et al. 1999 are used for each component of the periodic terms.

12. CONCLUSION Improved Algorithm for the Construction of the Non-Rigid Earth Rotation Series, which expressed in the function of the three Euler angles, are obtained.

13. R E F E R E N C E S 1.V.A..Brumberg, P.Bretagnon Kinematical Relativistic Corrections for Earth’s Rotation Parameters // in Proc. of IAU Colloquium 180, eds. K.Johnston, D. McCarthy, B. Luzum and G. Kaplan, U.S. Naval Observatory, 2000, pp. 293–302. 2.P.Bretagnon and G.Francou Planetary theories in rectangular and spherical variables //, Astronomy and Astrophysics, 202, 1988, pp. 309–-315. 3.P.Bretagnon, G.Francou, P.Rocher, J.L.Simon SMART97: A new solution for the rotation of the rigid Earth // Astron. Astrophys., 1998, 329, 1, pp.

14. A C K N O W L E D G M E N T S The investigation was carried out at the Central (Pulkovo) Astronomical Observatory of Russian Academy of Science and the Space Research Centre of Polish Academy of Science, under a financial support of the Cooperation between Polish and Russian Academies of Sciences, Theme No 31.