Hostname: page-component-5c6d5d7d68-wtssw Total loading time: 0 Render date: 2024-08-22T02:12:18.478Z Has data issue: false hasContentIssue false
  • English
  • Français

The Period of the Chandler Wobble

Published online by Cambridge University Press:  14 August 2015

F. A. Dahlen
F. A. Dahlen*
Affiliation:
Department of Geological and Geophysical Sciences, Princeton University, Princeton, New Jersey 08540 USA

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Realistic models of the Earth are known to possess a solid anelastic inner core, mantle and crust, and a fluid core and oceans. How might we go about calculating the theoretical free period of the Chandler wobble of such an Earth model? Let xi be a set of Cartesian axes with an origin at the center of mass, and let ωi be the instantaneous angular velocity of rotation of these axes with respect to inertial space. The net angular momentum is then Cijωj + hi, where Cij is the inertia tensor, and hi is the relative angular momentum. Let us affix the axes xi in the mantle and crust by stipulating that the relative angular momentum is that of the core and oceans alone, i.e., hi (mantle and crust) = 0; hi = hi (core and oceans). For an infinitesimal free oscillation of angular frequency σ, we can write ωi = Ω(δi3 + mi eiσt), Cij = A(δilδjl + δi2δj2) + Cδi3δj3 + cij eiσt, and hi = hi eiσt, where Ω is the mean rate of rotation and A and C are the mean equatorial and polar moments of inertia.

Type
Session IV
Information
Symposium - International Astronomical Union , Volume 78: Nutation and the Earth's Rotation , 1980 , pp. 187 - 193
Copyright
Copyright © Reidel 1980 

References

Akopyan, S. Ts., Zharkov, V. N., and Lyubimov, V. M.: 1975, Doklady Akad. Nauk 223, 87–89.Google Scholar
Akopyan, S. Ts., Zharkov, V. N., and Lyubimov, V. M.: 1976, Fizika Zemli No. 10, 3–12.Google Scholar
Currie, R. G.: 1974, Geophys. J. R. Astr. Soc. 38, 179–185.Google Scholar
Dahlen, F. A.: 1976, Geophys. J. R. Astr. Soc. 46, 363–406.Google Scholar
Gilbert, F. and Dziewonski, A. M.: 1975, Phil. Trans. R. Soc. Lond., Ser. A 278, 187–269.Google Scholar
Jeffreys, H.: 1968, Mon. Not. R. Astr. Soc. 141, 255–268.Google Scholar
Liu, H.-P., Anderson, D. L., and Kanamori, H.: 1976, Geophys. J. R. Astr. Soc. 47, 41–58.Google Scholar
Miller, S. P. and Wunsch, C.: 1973, Nature Phys. Sci. 246, 98–102.Google Scholar
Proudman, J.: 1960, Geophys. J. R. Astr. Soc. 3, 244–249.Google Scholar
Sailor, R. V. and Dziewonski, A. M.: 1977, EOS, Trans. Am. Geophys. Un. 58, 440.Google Scholar
Smith, M. L.: 1977, Geophys. J. R. Astr. Soc. 50, 103–140.Google Scholar
Wilson, C. R. and Haubrich, R. A.: 1976, Geophys. J. R. Astr. Soc. 46, 707–743.Google Scholar