A second order secular J-S planetary theory. Part I, Lemma

• Autorzy: Kamel, O. M. , Soliman, A. S.
• Języki publikacji: EN

Abstrakty

EN

A concise lemma is given for the construction of a semi-analytic Hamiltonian second order secular J-S planetary theory using the Jacobi-Radau system of origins and in terms of the non-singular variables of H. Poincaré. We truncate our expansions at the desired power in the eccentricities and the sines of the inclinations.

Słowa kluczowe

PL

dynamika Układu Słonecznego; teoria planetarna Hamiltona; mechanika nieba

EN

dynamics of the Solar system; Hamiltonian planetary theory; celestial mechanics

• Czasopismo: Mechanics and Mechanical Engineering
• Rocznik: 2018
• Tom: Vol. 22, nr 4
• Strony: 871--874
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Kamel, O. M.

• Astronomy and Space Sciences Department, Faculty of Sciences, Cairo University, Giza, Egypt,

autor

Soliman, A. S.

• Theoretical Physics Department, National Research Centre, Dokki, Giza, Egypt,

Bibliografia

• [1] Kamel, O.M.: MSc. Thesis submitted to the Faculty of Sciences, Cairo University, 1970.
• [2] Kael, O.M.: PhD. Thesis submitted to the Faculty of Sciences, Cairo University, 1973.
• [3] Brouwer, D. and Clemence, G.: Methods of Celestial Mechanics, Academic Press, 1965.
• [4] Smart, W.M.: Celestial Mechanics, Longmans, 1960.
• [5] Roy, A.E.: Orbital Motion, Fourth Edition, IOP Publishing Ltd., Bristol and Philadelphia, 2005.
• [6] Murray, C.D. and Dermott, S.F.: Solar System Dynamics, Cambridge University Press, 1999.
• [7] Kamel, O.M. and Bakry, A.A: Astrophysics and Space Science, Reidel, 78, 3-26, 1981.
• [8] Kamel, O.M.: The Moon and the Planets, Reidel, 26, 239-277, 1982.
• [9] Kamel, O.M. and Soliman, A.S.: Earth, Moon and Planets, Kluwer, 60, 141-175, 1993.
• [10] Jordan, D. and Smith, P.: Nonlinear Ordinary Differential Equations, Oxford University Press, Fourth Edition, 2007.
• [11] Jordan, D. and Smith, P.: Nonlinear Ordinary Differential Equations: Problems and Solutions, Oxford University Press, 2007.
• [12] Elmabsout, B. Kamel, O.M. and Soliman, A.S.: The expansion of the inverse of the mutual distance between two planets raised to any real integer using Taylor theorem and elliptic expansions, Part I, II, III submitted to Mechanics and Mechanical Engineering.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).