Abstract
This work is the first in the second part of a project dedicated to elaborating a Hamiltonian theory for the rotational motion of a deformable Earth. In the four works which make up the first part the basis of this theory is laid down, studying the effects produced when the Earth's elastic mantle is deformed by lunisolar attraction. More specifically, in Getino and Ferrándiz (1991), the elastic energy which is produced on the deformation of the Earth's mantle is studied, considering solely the second order in the development in spherical harmonics of the perturbing potential (tidal potential).
The present article can be considered as an amplification of the above mentioned, obtaining, under the same hypotheses, but also very general, the general expression of the said elastic energy for any order of the development of the tidal potential. Although at first this expression, in its general form, is very complicated, the final result is extremely simple, and for the case n = 2, it coincides, obviously, with that already found by the above mentioned authors.
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References
Bell, W.W.: 1968, ‘Special Functions for Scientists and Engineers’, Van Nostrand Company.
Getino, J.:1989, ‘Teoria Hamiltoniana del Movimiento de Rotación de una Tierra Deformable’, Ph.D. Thesis, University of Valladolid.
Getino, J. and Ferrándiz, J.M.: 1990, ‘A Hamiltonian Theory for an Elastic Earth: Canonical Variables and Kinetic Energy’, Celes. Mech. 49, 303–326.
Getino, J. and Ferrándiz, J.M.: 1991, ‘A Hamiltonian Theory for an Elastic Earth: Elastic Energy of Deformation’, Celes. Mech. 51, 17–34.
Gilbert, F. and Dziewonski, A.M.: 1975, Phil. Trans R. Soc. 287A, 187–269.
Jeffreys, H.: 1976, The Earth, Cambridge University Press.
Kaula, W.H.: 1966, Theory of Satellite Geodesy, Blaisdell, Waltham.
Kaula, W.M.: 1964, Rev. Geophys. 2 (4), 661–685.
Kaula, W.M.: 1969, Astron. J. 74 (9), 1108–1114.
Kinoshita, H.: 1977, Celes. Mech. 15, 277–326.
Kinoshita, H.: 1972, Publ. Astron. Soc. Japan 24, 423–457.
Kinoshita, H.: 1975, Smithsonian Astrophys., Obs. Special Report, No. 364.
Kubo, Y.: 1990, Private communication.
Love, A.E.H.: 1944, A Treatise on the Mathematical Theory of Elasticity, Dover, New York.
Melchior, P.: 1978, The Tides of the Planet Earth, Pergamon Press, Oxford.
Moritz, H.: 1982a, Bull. Géod. 56, 364–380.
Moritz, H.: 1982b, ‘Variational Methods in Earth Rotation’, in Moritz-Sunkel (ed.), Geodesy and Global Geodynamics, Mitteilungen Tech. Univ. Graz Folge 41.
Munk, W.H. and MacDonald G.J.: 1975, The Rotation of the Earth, Cambridge University Press.
Sokolnikoff, I.S.: 1956, Mathematical Theory of Elasticity, New York, McGraw-Hill.
Takeuchi, H.: 1950, Trans. Am. Geophys. Union 31(5), 651–689.
Vicente, R.O.: 1961, Physics and Chemistry of the Earth 4, 251–280.
Wahr, J.M.: 1979, ‘The Tidal Motions of a Rotating, Elastic and Oceanless Earth’, Ph.D. Thesis, Colorado.
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Getino, J. Elastic energy of a deformable earth: General expression. Celestial Mech Dyn Astr 53, 11–36 (1992). https://doi.org/10.1007/BF00049359
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DOI: https://doi.org/10.1007/BF00049359