Hamiltonian of a Second Order Two-Layer Earth Model

Selim, H. H.

doi:10.5303/jkas.2007.40.2.049

Cited by 2 publications

(3 citation statements)

References 15 publications

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“…Numerical of nutation series for the plane perpendicular to angular momentum vector and the plane perpendicular to figure axis of Earth will be carried out for the two cases of the present theories, tidal effect's forces coupling with the geopotential and the other by neglect the coupling between affecting forces. As mention before, we taking the approximation triaxial symmetry of Earth and using the other numerical coefficient listed in table 1 (Numerical coefficients) [10,17].…”

Section: Discussionmentioning

confidence: 99%

“…The numerical computations of the forced nutation for angular momentum axis eqns. (47), ( 48), ( 50), ( 51), ( 52), ( 53), ( 79), ( 80), ( 82), ( 83), ( 84), ( 85), ( 86) and (87) will be carried out by using the numerical coefficient in table 1 [10,17]. -0.00000 0.00000 -0.00000 0.00000 -0.00000 -0.00000 409.23 0.00000 0.00000 0.00000 0.00000 -0.00000 0.00000 365.26 0.00000 -0.00000 0.00000 0.00000 0.00000 0.00000 212.32 -0.00000 0.00000 -0.00000 0.00000 -0.00000 -0.00000 182.62 -0.00003 -0.00014 -0.00016 -0.00014 0.00014 -0.00000 121.75 -0.00000 -0.00001 -0.00001 -0.00001 0.00001 -0.00000 117.54 -0.00000 0.00000 -0.00000 0.00000 -0.00000 -0.00000 -32.61 0.00000 -0.00000 0.00000 -0.00000 0.00000 -0.00000 29.53 -0.00000 0.00000 -0.00000 0.00000 -0.00000 -0.00000 -27.33 0.00000 0.00000 0.00000 0.00000 -0.00000 -0.00000 -0.00000 -0.00000 -0.00000 -0.00000 182.62 -0.00000 -0.00000 0.00000 0.00000 121.75 -0.00000 -0.00000 0.00000 0.00000 117.54 -0.00000 -0.00000 0.00000 0.00000 -32.61 0.00000 0.00000 0.00000 0.00000 29.53 -0.00000 -0.00000 0.00000 0.00000 -27.33 0.00000 0.00000 -0.00000 -0.00000…”

Section: Numerical Representation Of Nutation Seriesmentioning

confidence: 99%

“…Because of Earth is responds to any effect to be as a deformable body and not as a strictly rigid, it is possesses some sort of elastic properties [1]. Many papers concerned with the study of a rotation for a deformable Earth through different theories of Earth's model as the series of papers [2][3][4][5][6] and another series [7][8][9][10][11][12][13]. So, its shape changes through the rotational motion about its axis, this change affects on the periodic rotation and its uniformity, which intern affects on its shape, also, the same done due to the tidal effects of Sun and Moon.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Forced Nutation for Rigid Earth Model with Different Theories

Soliman¹,

Selim²,

Hassan³

2019

IJAMTP

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Where Earth is not strictly rigid body but can responds to any effects that tend to its rotation and shape, we will explain, in the present paper, the goal which is to define the forced nutation for a rigid Earth model using two different theories. We will formulate a first order Hamiltonian of a deformable Earth for its rotational motion around the Sun through the contribution of triaxial symmetry of the Earth. The formulation of the theory will be formed twice times. Firstly, deduce the tidal affect's forces by Luni -Solar attraction coupling with the Earth's geopotential force. Secondly, through the formulation, we will neglect the coupling between the different effects (the geopotential Earth force effect and the Luni -Solar attraction force), so, we will find the transform of the Hamiltonian for each force separately. The analytical solution for the formulated Hamiltonian will be derived for the two cases by using perturbation technique of Lie -Hori series. Once can get the analytical solution by getting the generation function, we will derive the nutation series analytically and numerically for each case and conclude over the results.

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Section: Discussionmentioning

confidence: 99%

Section: Numerical Representation Of Nutation Seriesmentioning

confidence: 99%