Solution to the rotation of the elastic earth by method of rigid dynamics

Kubo, Yoshio

doi:10.1007/bf00051048

Cited by 19 publications

(79 citation statements)

References 4 publications

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“…We also present in the same table other useful quantities, such as constants and geodetic parameters, considered in the present paper. For this purpose, we have chosen the same notation as in Kinoshita (1977), Moritz & Mueller (1987), Kubo (1991) and Souchay et al (2002) in order to establish homogeneity of notation. The interested reader is referred to the above mentioned articles and textbook for more details.…”

Section: Notation and Definitionsmentioning

confidence: 99%

“…The Hamiltonian formulation for the rotation of an elastic body such as the Earth has been discussed in detail by, to the best of our knowledge, Sevilla & Romero (1985), Getino & Ferrándiz (1990, 1991, Kubo (1991) and Stavinschi & Souchay (1994). In this study, we have followed Kubo's procedure and we have amplified some aspects of his presentation, considering a triaxial body instead of a body with rotational symmetry.…”

Section: Introductionmentioning

confidence: 99%

“…During the thirteen years that have passed since Kubo (1991), the level of accuracy in the observational techniques, such VLBI (Very Long Baseline Interferometry), GPS (Global Positioning System) and LLR (Lunar Laser Ranging), has increased enormously. As an application of the theoretical developments above, we not only show that at the level of 1 mas some variations related to the triaxial shape of the Earth and generally not considered have to be taken into account at the present date.…”

Section: Introductionmentioning

confidence: 99%

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Free polar motion of a triaxial and elastic body in Hamiltonian formalism: Application to the Earth and Mars

Folgueira¹,

Souchay²

2005

A&A

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Abstract. The purpose of this paper is to show how to solve in Hamiltonian formalism the equations of the polar motion of any arbitrarily shaped elastic celestial body, i.e. the motion of its rotation axis (or angular momentum) with respect to its figure axis. With this aim, we deduce from canonical equations related to the rotational Hamiltonian of the body, the analytical solution for its free polar motion which depends both on the elasticity and on its moments of inertia. In particular, we study the influence of the phase angle δ, responsible for the dissipation, on the damping of the polar motion. In order to validate our analytical equations, we show that, to first order, they are in complete agreement with those obtained from the classical Liouville equations. Then we adapt our calculations to the real data obtained from the polar motion of the Earth (polhody). For that purpose, we characterize precisely the differences in radius J − χ and in angle l − θ between the polar coordinates (χ, θ) and (J, l) representing respectively the motion of the axis of rotation of the Earth and the motion of its angular momentum axis, with respect to an Earth-fixed reference frame, after showing the influence of the choice of the origin on these coordinates, and on the determination of the Chandler period as well. Then we show that the phase lag δ responsible for the damping for the selected time interval, between Feb. 1982 and Apr. 1990, might be of the order of δ ≈ 6• , according to a numerical integration starting from our analytical equations. Moreover, we emphasize the presence in our calculations for both χ and θ, of an oscillation with a period T Chandler /2, due to the triaxial shape of our planet, and generally not taken into account. In a last step, we apply our analytical formulation to the polar motion of Mars, thus showing the high dependence of its damping on the poorly known value of its Love number k. Moreover we emphasize the large oscillations of Mars' polar motion due to the triaxiality of this planet.

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Section: Notation and Definitionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Free polar motion of a triaxial and elastic body in Hamiltonian formalism: Application to the Earth and Mars

Folgueira¹,

Souchay²

2005

A&A

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“…where 6 is the angle of delay (Getino & Ferrandiz 1991;Kubo, 1991). Solution of equations (12) l -t a n 2 f t ( « -i 0 ) sin #o (13)…”

Section: Damping Of the Chandler Polar Motionmentioning

confidence: 99%

Nature and Properties of the Chandler Motion and Mechanism of its Damping and Excitation

Ferrándiz

Barkin²

2000

International Astronomical Union Colloquium

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Abstract. The analytical studies of the Chandler motion of the Earth's pole on the basis of the special approach to the problem, using the canonical and noncanonical equations in the Andoyer elastic variables Barkin, 1996; in press) have been fulfilled. The Earth is considered as an isolated celestial body with the anelastic (in general case) external envelope (the mantle) and an invariant central part (the core).

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“…A full description of these variables is given in the papers by Kinoshita (1977), Getino and Ferrandiz (1990), Kubo (1991), and Barkin (1999). In the last papers the differential equations of rotational motion of a weakly deformable body in the Andoyer variables were obtained in the general case.…”

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confidence: 99%

Tidal Variations of the Earth Rotation

Ferrándiz

Barkin

Getino

2000

International Astronomical Union Colloquium

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Abstract. The equations for the rotation of a weakly deformable celestial body in non canonical Andoyer variables have been used to study the perturbation of Earth rotation due to tidal deformation raised by the Moon and Sun. A theory of the perturbed rotational motion of an isolated weakly deformable body in Andoyer variables and in components of the angular velocity has been developed. Mantle tidal deformations due to lunar and solar influences were analytically described and taken into account. Perturbations of the first order in the Earth's polar motion were determined.

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Solution to the rotation of the elastic earth by method of rigid dynamics

Cited by 19 publications

References 4 publications

Free polar motion of a triaxial and elastic body in Hamiltonian formalism: Application to the Earth and Mars

Free polar motion of a triaxial and elastic body in Hamiltonian formalism: Application to the Earth and Mars

Nature and Properties of the Chandler Motion and Mechanism of its Damping and Excitation

Tidal Variations of the Earth Rotation

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