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IssuesArchive of Issues2012-6pp.601-621

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L.D. Akulenko, D.M. Klimov, Yu.G. Markov, and V.V. Perepelkin, "Oscillatory-Rotational Processes in the Earth Motion about the Center of Mass: Interpolation and Forecast," Mech. Solids. 47 (6), 601-621 (2012)
Year 2012 Volume 47 Number 6 Pages 601-621
DOI 10.3103/S0025654412060015
Title Oscillatory-Rotational Processes in the Earth Motion about the Center of Mass: Interpolation and Forecast
Author(s) L.D. Akulenko (Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str. 1, Moscow, 119526 Russia, bolotnik@ipmnet.ru)
D.M. Klimov (Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str. 1, Moscow, 119526 Russia, klimov@ipmnet.ru)
Yu.G. Markov (Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str. 1, Moscow, 119526 Russia, markov@ipmnet.ru)
V.V. Perepelkin (Moscow Aviation Institute (State University of Aerospace Technologies), Volokolamskoe sh. 4, GSP-3, A-80, Moscow, 125993 Russia, vadimkin1@yandex.ru)
Abstract The celestial-mechanics approach (the spatial version of the problem for the Earth-Moon system in the field of gravity of the Sun) is used to construct a mathematical model of the Earth's rotational-oscillatory motions. The fundamental aspects of the processes of tidal inhomogeneity in the Earth rotation and the Earth's pole oscillations are studied. It is shown that the presence of the perturbing component of gravitational-tidal forces, which is orthogonal to the Moon's orbit plane, also allows one to distinguish short-period perturbations in the Moon's motion. The obtained model of rotational-oscillatory motions of the nonrigid Earth takes into account both the basic perturbations of large amplitudes and the more complicated small-scale properties of the motion due to the Moon short-period perturbations with combination frequencies.

The astrometric data of the International Earth Rotation and Reference Systems Service (IERS) are used to perform numerical simulation (interpolation and forecast) of the Earth rotation parameters (ERP) on various time intervals.
Keywords the Earth rotation inhomogeneities, center of mass, viscoelastic model, gravitational-tidal perturbations, oscillations of poles, day length, time scale, Universal Time
References
1.  IERS Annual Reports, URL: http://www.iers.org.
2.  E. W. Woolard, Theory of the Rotation of the Earth around Its Center of Mass (Astron. Pap. Amer. Eph. Naut. Almanac XV (1), 1-165 (1953); Fizmatgiz, Moscow, 1963).
3.  W. H. Munk and G. J. F. MacDonald, The Rotation of the Earth (Cambridge Univ. Press, Cambridge, 1960; Mir, Moscow, 1964).
4.  H. Moritz and I. I. Mueller, Earth Rotation: Theory and Observations (Ungar, New York, 1987; Naukova Dumka, Kiev, 1992).
5.  J. Vondrak, "Earth Rotation Parameters 1899.7-1992.0 after Reanalysis within the Hipporcos Frame," Surv. Geophys. 20, 169-195 (1999).
6.  C. Audoin and B. Guinot, The Measurement of Time: Time, Frequency, and the Atomic Clock (Masson, Paris, 1998; Cambridge Univ. Press, Cambridge, 2001; Tekhnosfera, Moscow, 2002).
7.  N. S. Sidorenkov, Physics of the Earth's Rotation Instabilities (Nauka, Fizmatlit, Moscow, 2002).
8.  L. D. Akulenko, S. A. Kumakshev, and Yu. G. Markov, "Modeling of the Pole's Motion for the Deformable Earth," Dokl. Ross. Akad. Nauk 379 (2), 191-195 (2001) [Dokl. Phys. (Engl. Transl.) 46, 508-512 (2001)].
9.  L. D. Akulenko, S. A. Kumakshev, Yu. G. Markov, and L. V. Rykhlova, "A Gravitational-Tidal Mechanism for the Earth's Polar Oscillations," Astron. Zh. 82 (10), 950-960 (2005) [Astron. Rep. (Engl. Transl.) 49 (10), 847-857 (2005)].
10.  L. D. Akulenko, S. A. Kumakshev, Yu. G. Markov, and L. V. Rykhlova, "Analysis of Multifrequency Effects in Oscillations of the Earth's Pole," Astron. Zh. 84 (5), 471-478 (2007) [Astron. Rep. (Engl. Transl.) 51 (5), 421-427 (2007)].
11.  V. V. Bondarenko and V. V. Perepelkin, "Rotational-Oscillational Motions of the Nonrigid Earth about the Center of Mass," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 5, 25-35 (2009) [Mech. Solids (Engl. Transl.) 44 (5), 677-685 (2009)].
12.  L. D. Akulenko, Yu. G. Markov, and V. V. Perepelkin, "A Celestial Mechanics Model of the Earth's Rotation Irregularity," Kosmich. Issled. 47 (5), 452-459 (2009) [Cosmic Res. (Engl. Transl.) 47 (5), 417-425 (2009)].
13.  L. D. Akulenko, Yu. G. Markov, and V. V. Perepelkin, "Dynamical Analysis of Subtle Effects of the Earth's Tidal Rotation Irregularity," Dokl. Ross. Akad. Nauk 436 (1), 38-42 (2011) [Dokl. Phys. (Engl. Transl.) 56 (1), 16-21 (2011)].
14.  L. D. Akulenko, Yu. G. Markov, and V. V. Perepelkin, "Modeling of the Earth's Rotary-Oscillatory Motion within a Short Time Interval (Interpolation and Prognosis)," Dokl. Ross. Akad. Nauk 438 (3), 326-331 (2011) [Dokl. Phys. (Engl. Transl.) 56 (5), 294-299 (2011)].
15.  V. S. Gubanov, Generalized Least Squares Method. Theory and Applications in Astrometry (Nauka, St. Petersburg, 1997) [in Russian].
16.  W. Smart, Celestial Mechanics (Wiley, New York, 1961; Mir, Moscow, 1965).
Received 29 March 2012
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