Non-Rigid Rotation, Global Geodynamics and Free Nutation

ABSTRACT

The rotation of the physical Earth not only obeys the law of conservation of angular momentum but follows also the three-finger rule of the right-handed system. The reference frame in the Earth is most essential. The generalized Eulerian equation of motion or the Liouville equation is to represent global geodynamics in general, which is examined directly through the observation of the Earth’s rotation and surface motions, with no additional assumptions after fundamental physics. Rotational acceleration, polar motion, plate tectonics, and seismicity observed on the Earth’s surface indicate that the Earth’s angular momentum is perturbed and adjusting independently of external torques. (For more information,please refer to the PDF.)

Cite this paper

Pan, C. (2014) Non-Rigid Rotation, Global Geodynamics and Free Nutation.*International Journal of Geosciences*, **5**, 63-76. doi: 10.4236/ijg.2014.51008.

Pan, C. (2014) Non-Rigid Rotation, Global Geodynamics and Free Nutation.

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http://dx.doi.org/10.1016/j.jog.2006.12.004

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http://dx.doi.org/10.4236/ijg.2012.325095

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[1] C. Pan, “Observed Multiple Frequencies of the Chandler Wobble,” Journal of Geodynamics, Vol. 44, No. 1-2, 2007, pp. 47-65.

http://dx.doi.org/10.1016/j.jog.2006.12.004

[2] C. Pan, “Linearization of the Liouville Equation, Multiple Splits of the Chandler Frequency, Markowitz Wobbles, and Error Analysis,” International Journal of Geosciences, Vol. 3, No. 2, 2012, pp. 930-951.

http://dx.doi.org/10.4236/ijg.2012.325095

[3] T. Thomson, “Introduction to Space Dynamics,” Wiley, New York, 1986, 317 p.

[4] R. E. Roberson, “The Equivalence of Two Classical Problems of Free Spinning Gyrostats,” Journal of Applied Mechanics, Vol. 38, No. 3, 1971, pp. 707-708.

[5] G. M. T. D’Eleuterio and P. C. Hughes, “Dynamics of a Flexible Vehicle with a General Angular Momentum distribution,” Progress Report at the III PVI and SU/AIAA Symposium on the Dynamics and Control of Large Flexible Spacecraft, Blacksburg, Virginia, 1981.

[6] H. B. Hablani, “Modal Analysis of Gyroscopic Flexible Spacecraft: A Continuum Approach,” Guidance, Control and Dynamics, Vol. 5, No. 5, 1982, pp. 448-457.

[7] G. M. T. D’Eleuterio and P. C. Hughes, “Dynamics of Gyro-Elastic Continua,” AIAA/ASME/ASCE/AHS 24th Structures, Structural Dynamics & Materials Conference, 2-4 May 1983, 1983, 9 p.

[8] H. Rance, “Major Lineaments and Torsional Deformation of the Earth,” Journal of Geophysical Research, Vol. 72, No. 8, 1968, pp. 2213-2217.

http://dx.doi.org/10.1029/JZ072i008p02213

[9] H. Rance, “Lineaments and Torsional Deformation of the Earth: Indian Ocean,” Journal of Geophysical Research, Vol. 74, No. 12, 1969, pp. 3271-3272.

http://dx.doi.org/10.1029/JB074i012p03271

[10] B. F. Howell Jr., “Coriolis Force and the New Global Tectonics,” Journal of Geophysical Research, Vol. 75, No. 14, 1970, pp. 2769-2772.

http://dx.doi.org/10.1029/JB075i014p02769

[11] M. F. Kane, “Rotational Inertia of Continents: A Proposed Link between Polar Wandering and Plate Tectonics,” Science, Vol. 175, No. 4028, 1972, pp. 1355-1357.

http://dx.doi.org/10.1126/science.175.4028.1355

[12] K. W. Hudnut, “Geodetic Evidence for the Rotation of Crustal Blocks (Abstract), EOS,” Transactions— American Geophysical Union, Vol. 72, 1991, p. 124.

[13] D. E. Argus, and R. G. Gordon, “Rotation of the Sierra Nevada from VLBI data (Abstract), EOS,” Transactions—American Geophysical Union, Vol. 72, 1991, p. 124.

[14] C. Pan, “Polar Motion of a Triaxial Earth and Dynamical Plate Tectonics,” Tectonophysics, Vol. 25, No. 1-2, 1975, pp. 1-40.

http://dx.doi.org/10.1016/0040-1951(75)90009-8

[15] C. Pan, “Polar Instability, Plate Motion, and Geodynamics of the Mantle,” Journal of Physics of the Earth, Vol. 33, No. 5, 1985, pp. 411-434.

http://dx.doi.org/10.4294/jpe1952.33.411

[16] C. Pan, “The Multiple-Frequency Chandler Wobble,” Journal of Physics of the Earth, Vol. 30, No. 5, 1982, pp. 389-419. http://dx.doi.org/10.4294/jpe1952.30.389

[17] C. Pan, “Angular Momentum Perturbation, Polar Excitation, and Axial Near-Symmetry,” Geophysical Journal International, Vol. 137, No. 1, 1999, pp. 139-148.

http://dx.doi.org/10.1046/j.1365-246x.1999.00782.x

[18] W. H. Munk and G. J. F. MacDonald, “The Rotation of the Earth,” Cambridge University Press, London, 1960, 323 p.

[19] B. F. Chao, “On the Excitation of the Earth’s Free Wobble and Reference Frames,” Geophysical Journal International, Vol. 79, No. 2, 1984, pp. 555-563.

http://dx.doi.org/10.1111/j.1365-246X.1984.tb02240.x

[20] H. Moritz and I. I. Mueller, “Earth Rotation: Theory and Observation,” The Ungar Publishing Company, New York, 1988, 617 p.

[21] M. L. Smith, “Wobble and Nutation of the Earth,” Geophysical Journal International, Vol. 50, No. 1, 1977, pp. 103-140. http://dx.doi.org/10.1111/j.1365-246X.1977.tb01326.x

[22] K. Lambeck, “The Earth’s Variable Rotation: Geophysical Causes and Consequences,” Cambridge University Press, London, 1980, 449 p.

http://dx.doi.org/10.1017/CBO9780511569579

[23] R. A. Becker, “Introduction to Theoretical Mechanics,” McGraw-Hill, New York, 1954, 420 p.

[24] C. Pan, “The Earth’s Rotation Instability, Plate Motion, and Geodynamics of the Mantle (Abstract),” AGU Transactions, Vol. 59, 1978, pp. 1202-1203.

[25] F. M. Richter, “Dynamical Model for Sea-Floor Spreading,” Reviews of Geophysics, Vol. 11, No. 2, 1973, pp. 223-287. http://dx.doi.org/10.1029/RG011i002p00223

[26] W. Markowitz, “Sudden Changes in Rotational Acceleration of the Earth and Secular Motion of the Pole,” In: L. Mansinha, D. E. Smylie and A. E. Beck, Eds., Earthquake Displacement Fields and the Rotation of the Earth, Reidel, Dordrecht, 1970, pp. 69-81.

http://dx.doi.org/10.1007/978-94-010-3308-4_7

[27] W. Markowitz, “Rotational Accelerations,” In: P. Melchior and S. Yumi, Eds., Rotation of the Earth, IAU Symposium No. 48, Reidel, Dordrecht, 1972, pp. 162-164.

[28] K. Lambeck, “Effects of Tidal Dissipation in the Oceans on the Moon’s Orbit and the Earth’s Rotation,” Journal of Geophysical Research, Vol. 80, No. 20, 1975, pp. 2917-2925. http://dx.doi.org/10.1029/JB080i020p02917

[29] K. Lambeck, “Tidal Dissipation in the Oceans: Astronomical, Geophysical and Oceanographic Consequences, Philos,” Transactions of the Royal Society London A, Vol. 287, 1347, 1977, pp. 545-594.

http://dx.doi.org/10.1098/rsta.1977.0159

[30] K. Lambeck and A. Cazenave, “The Earth’s Rotation and Atmosphere Circulation—I. Seasonal Variations,” Geophysical Journal of the Royal Astronomical Society, Vol. 32, 1973, pp. 79-93.

[31] K. Lambeck and A. Cazenave, “The Earth’s Variable Rate of Rotation: A Discussion of Some Meteorological and Oceanic Causes and Consequences,” Philosophical Transactions of the Royal Society London A, Vol. 284, No. 1326, 1977, pp. 495-506.

http://dx.doi.org/10.1098/rsta.1977.0025

[32] L. V. Morrison, “Tidal Deceleration of the Earth’s Rotation Deduced from Astronomical Observations in the Period A. D. 1600 to the Present,” In: P. Brosche and J. Sunderman, Eds., Tidal Friction and the Earth’s Rotation, Springer-Verlag, Berlin, 1978, pp. 22-27.

[33] W. Alvarez and F. Asaro, “An Extraterrestrial Impact,” Scientific American, Vol. 263, No. 4, 1990, pp. 78-84.

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