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1

RERS2014 and MRS2014: new high-precision rigid Earth rotation and Moon rotation series

Pashkevich V. V.

Artificial Satellites : Journal of Planetary Geodesy

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2015

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Vol. 50, No. 1

35--40

EN

Numerical investigation of the Earth and Moon rotational motion dynamics is carried out at a long time intervals. In our previous studies (Pashkevich, 2013), (Pashkevich and Eroshkin, 2011) the high-precision Rigid Earth Rotation Series (designated RERS2013) and Moon Rotation Series (designated MRS2011) were constructed. RERS2013 are dynamically adequate to the JPL DE422/LE422 (Folkner, 2011) ephemeris over 2000 and 6000 years and include about 4113 periodical terms (without attempt to estimate new subdiurnal and diurnal periodical terms). MRS2011 are dynamically adequate to the JPL DE406/LE406 (Standish, 1998) ephemeris over 418, 2000 and 6000 years and include about 1520 periodical terms. In present research have been improved the Rigid Earth Rotation Series RERS2013 and Moon Rotation Series MRS2011, and as a result have been constructed the new high-precision Rigid Earth Rotation Series RERS2014 and Moon Rotation Series MRS2014 dynamically adequate to the JPL DE422/LE422 ephemeris over 2000 and 6000 years, respectively. The elaboration of RERS2013 is carried out by means recalculation of sub-diurnal and diurnal periodical terms. The residuals in Euler angles between the numerical solution and RERS2014 do not surpass 3 μas over 2000 years. Improve the accuracy of the series MRS2011 is obtained by using the JPL DE422/LE422 ephemeris. The residuals in the perturbing terms of the physical librations between the numerical solution and MRS2014 do not surpass 8 arc seconds over 6000 years.

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RERS2013: a new high-precision rigid Earth rotation series

Pashkevich V. V.

Artificial Satellites : Journal of Planetary Geodesy

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2014

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Vol. 49, No. 3

161--177

EN

In the previous investigation (Pashkevich, 2013) the high-precision Rigid Earth Rotation Series (designated RERS2012) dynamically adequate to the JPL DE406/LE406 (Standish, 1998) ephemeris over 2000 and 6000 years were constructed. The main aim of present research is improvement of the Rigid Earth Rotation Series RERS2012 by using the JPL DE422/LE422 (Folkner, 2011) ephemeris, and as a result is produced construction of the new high-precision Rigid Earth Rotation Series dynamically adequate to the JPL DE422/LE422 ephemeris over 2000 and 6000 years. The discrepancies in Euler angles between the high-precision numerical solutions and the semi-analytical solutions of the rigid Earth rotation problem are investigated by least squares and spectral analysis methods using the iterative algorithm (Pashkevich, 2013). In order to demonstrate the good convergence of this iterative algorithm are constructed additional solutions of the rigid Earth rotation dynamically adequate to the JPL DE422/LE422 over 2000 years by improvement solutions SMART97 (Bretagnon et al., 1998) and S9000 (Pashkevich and Eroshkin, 2005a). As the results of this investigation, the new improved high-precision Rigid Earth Rotation Series RERS2013 dynamically adequate to the DE422/LE422 ephemeris over 2000 and 6000 years have been constructed. The discrepancies in Euler angles between the numerical solution and RERS2013 do not surpass: 4 as over 2000 years, 1 mas over 6000 years. The RERS2013 series is more accurate than the RERS2012 series, which is dynamically adequate to the DE406/LE406 ephemeris. The good convergence of the iterative algorithm of this study has been confirmed.

3

Construction of the numerical and semi-analytical solutions of the rigid Earth rotation at a long time intervals

Pashkevich V. V.

Artificial Satellites : Journal of Planetary Geodesy

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2013

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Vol. 48, No. 1

25--37

EN

This research is the continuation of our studies of the rigid Earth rotation at a long time intervals (Pashkevich V.V. and Eroshkin G.I., 2005). The main purpose of this investigation is the construction of the new high-precision Rigid Earth Rotation Series 2012 (RERS2012), dynamically adequate to the JPL DE406/LE406 ephemeris (Standish E. M., 1998). The dynamics of the rotational motion of the rigid Earth is studied numerically by using Rodrigues-Hamilton parameters over 2000 and 6000 years. The numerical solution of the rigid Earth rotation is implemented with the quadruple precision of the calculations. The orbital motions of the disturbing celestial bodies are defined by the DE406/LE406 ephemeris. The initial conditions of the numerical integration are taken from SMART97 (Bretagnon P. et al., 1998) and S9000 (Pashkevich V.V. and Eroshkin G.I. 2005). The results of the numerical solutions of the problem are compared with the semi-analytical solutions of the rigid Earth rotation (SMART97 and S9000, respectively) with respect to the fixed ecliptic of epoch J2000. The investigation of these discrepancies is carried out by the least squares and spectral analysis methods for the relativistic (Kinematical) case, in which the geodetic perturbations (the most essential relativistic perturbations) in the Earth rotation are taken into account. As a result, the Rigid Earth Rotation Series (RERS2012) is constructed, which is dynamically adequate to the DE406/LE406 ephemeris over 2000 and 6000 years. The discrepancies between the new numerical solutions and the semi-analytical solutions of MRS2012 do not surpass 12 μas over 2000 year time interval and 2 mas over 6000 year time interval. Thus, the result of the comparison demonstrates a good consistency of RERS2012 series with the DE406/LE406 ephemeris.

4

Construction of the new high-precision Moon rotation series at a long time intervals

Pashkevich V. V., Eroshkin G. I.

Artificial Satellites : Journal of Planetary Geodesy

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2011

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Vol. 46, No. 2

63--73

EN

The main purposes of this research are the construction of the new highprecision Moon Rotation Series (MRS2011), dynamically adequate to the DE404/LE404 and the DE406/LE406 ephemeris, over long time intervals. The comparison of the new highprecision Moon Rotation solutions of MRS2011 with the solution of MRS2010 (Pashkevich and Eroshkin, 2010), which is dynamically adequate to the DE200/LE200 ephemeris over 418.9 year time interval, is performed. The dynamics of the rotational motion of the Moon is studied numerically by using Rodrigues-Hamilton parameters over 418.9, 2000 and 6000 years. The numerical solution of the Moon rotation is implemented with the quadruple precision of the calculations. The results of the numerical solution of the problem are compared with the composite semi-analytical theory of the Moon rotation (SMR) (Pashkevich and Eroshkin, 2010) with respect to the fixed ecliptic of epoch J2000. The initial conditions of the numerical integration are taken from SMR. The investigation of the discrepancies is carried out by the least squares and spectral analysis methods for the Newtonian case. All the secular, periodic and Poisson terms, representing the behavior of the residuals, are interpreted as corrections to SMR semi-analytical theory. As a result, the Moon Rotation Series (MRS2011) is constructed, which is dynamically adequate to the DE404/LE404 and the DE406/LE406 ephemeris over 418.9, 2000 and 6000 years. A numerical solution for the Moon rotation is obtained anew with the new initial conditions calculated by means of MRS2011. The discrepancies between the new numerical solution and the semi-analytical solution of MRS2011 do not surpass 20 mas over 418.9 year time interval, 64 mas over 2000 year time interval and 8 arc seconds over 6000 year time interval. Thus, the result of the comparison demonstrates a good consistency of MRS2011 series with the DE/LE ephemeris.

5

FFT-based spectral dynamic analysis for linear discrete dynamic systems

Lee U., Cho J.

Journal of Achievements in Materials and Manufacturing Engineering

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2007

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Vol. 25, nr 1

95-102

EN

Purpose: An FFT-based spectral dynamic analysis method is developed for the viscously damped, linear discrete dynamic systems subjected to nonzero initial conditions. Design/methodology/approach: The discrete Fourier transform (DFT) theory is used to develop a spectral dynamic analysis method. The dynamic response of a linear system is assumed as the sum of the forced and free vibration response parts. The forced vibration response part is obtained by convolving the dynamic stiffness matrix and Fourier components of excitation force through the Duhamel's integral, and the free vibration response part is obtained by determining its integral constants so as to satisfy initial conditions in frequency-domain. Findings: It is shown through some numeral examples that the proposed FFT-based spectral dynamic analysis method provides the solutions which accurately satisfy all initial conditions. Practical implications: This analysis method is applicable to viscously damped, linear discrete dynamic systems subjected to nonzero arbitrary initial conditions. In this study, two types of viscous damping are considered: proportional damping and non-proportional damping. Originality/value: The FFT-based spectral dynamic analysis method proposed in this paper is unique because the pseudo-force concept or the superposition of corrective free vibration solution used by other researchers is not used to take into account non-zero initial conditions.

6

Dynamic response with arbitrary initial conditions using the FFT

Lee U., Cho J.

Journal of Achievements in Materials and Manufacturing Engineering

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2006

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Vol. 18, nr 1-2

299--302

EN

Purpose: An FFT-based dynamic analysis method is proposed for damped linear discrete dynamic systems subjected to arbitrary nonzero initial conditions. Design/methodology/approach: The DFT theory is used to develop an FFT-based spectral analysis method. The total dynamic response is considered as the sum of the forced vibration response part and the free vibration response part. The forced vibration response part is obtained from the dynamic stiffness matrix and the Fourier components of excitation force based on the concept of Duhamel’s integral, and the free vibration response part is obtained by determining its integral constant to satisfy arbitrary initial conditions in the frequency-domain. Findings: Through some numeral examples, the proposed FFT-based dynamic analysis method is shown to provide very successful solutions which satisfy all arbitrary non-zero initial conditions. Research limitations/implications: (not applicable). Practical implications: (not applicable). Originality/value: The present FFT-based method is unique because it does not use the superposition of corrective free vibration solution or the pseudo-force concept used by other researchers to take into account the non-zero initial conditions.