#### For citation:

Ivashchenko N. N., Sidorenkov N. S., Sonechkin D. M. Study of the earth’s pole motion using a mapping on an external force period. *Izvestiya VUZ. Applied Nonlinear Dynamics*, 2007, vol. 15, iss. 4, pp. 84-91. DOI: 10.18500/0869-6632-2007-15-4-84-91

# Study of the earth’s pole motion using a mapping on an external force period

It is known from astronomic observations that the motions of the North pole of the Earth consist of a trend to the Greenland direction, and a rotational component superimposed on the trend. The periods of 12 and about 14 months these motions. The first period is resulted from the seasonal mass redistribution in atmosphere and oceans. The second period is its called the Chandlerian and nature is vague. Because of incommensurability of both periods each with another one can see six/sevel year beats in the time series of the Earth’s pole coordinates. It is not known definitely what is the character of these beats. The aim of this paper is to clear up this question using the most accurate time series of the North pole coordinates covering the time from 5 January 1962 up to 18 July 2004 (sampled over 5 day period). A mathematical technique of mapping is used for the phase trajectory section chosen at the annual period of the external force. It is found that the beat frequency varies by a quasi-periodic manner, and the beat amplitude is seasonal dependent one.

- Euler L. Collection of articles in honor of the 250th anniversary of his birth. Moscow: Academy of Sciences of the USSR; 1958. (in Russian).
- Chandler C. On the variation of the latitude. Astron. J. 1891;248:59-61.
- Avsyuk YuN. The Tidal Forces and Natural Processes. Moscow: Schmidt Joint Institute of Physics of the Earth, Russ. Acad. Sci.; 1966. (in Russian).
- Arato M. Linear stochastic systems with constant coefficients. Statistical approach. Moscow: Nauka; 1989.
- Hoepfner J. Low-frequency variations, Chandler and annual wobbles of polar motion as observed over one century. Surveys in Geophysics. 2004;25:1–54. DOI: 10.1023/B:GEOP.0000015345.88410.36.
- Munk W, Macdonald G. The rotation of the Earth. Moscow: Mir; 1968. (in Russian).
- Monin AS. Rotation of the Earth and climate. Leningrad: Hydrometeoizdat; 1972. (in Russian).
- Sidorenkov NS. Physics of the Earth Rotation Instabilities. Moscow: Fizmatlit; 2002. (in Russian).
- Legros H, Amalvict M. Rotation of a deformable Earth with dynamical superficial fluid layer and liquid core. Part 1: Fundamental equations. Annales Geophysicae. 1985;3(5):655–670.
- Greff-Lefftz M, Legros H. Magnetic field and rotational eigenfrequencies. Physics of the Earth and Planetary Interiors. 1999;112:21–41. DOI: 10.1016/S0031-9201(98)00154-X.
- Sonechkin DM. Nonlinear nature of the Chandler Wobble in the Earth's pole motion. Doklady Earth Sciences. 2001;381A:1107–1109.
- Ivashchenko NN, Sidorenkov NS, Sonechkin DM. Evidence of nonlinearity of the chandler wobble in the Earth's pole motion. Doklady Earth Sciences. 2006;409(5):801–804. DOI: 10.1134/S1028334X0605028X.
- Butenin NV, Neimark YuI, Fufaev NA. Introduction to Nonlinear Oscillations. Moscow: Nauka; 1976. (in Russian).
- Kurbasova GS, Korsun' AA, Rykhlova LV, Rybalova MN, Shlikar' GN. A comparison of low-frequency variations in two data series on the coordinates of the Earth's pole. Astronomy Reports. 1997;41(5):699–704.
- Kurbasova GS, Rykhlova LV. Identification of the regime of the polar motion using coordinate data for 1900-1990. Astronomy Reports. 1998;42(4):558–565.
- Sidorenkov NS. Mechanisms of interannual variability of the atmosphere and ocean. Proceedings of the Hydrometeorological Center of Russia. 2000;335:26–41. (in Russian).

- 1624 reads