Deprit, Andre Delaunay normalisations. (English) Zbl 0512.70016 Celestial Mech. 26, 9-21 (1982). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 25 Documents MSC: 70F15 Celestial mechanics 70M20 Orbital mechanics 70-02 Research exposition (monographs, survey articles) pertaining to mechanics of particles and systems 70H05 Hamilton’s equations 70H15 Canonical and symplectic transformations for problems in Hamiltonian and Lagrangian mechanics 17B99 Lie algebras and Lie superalgebras Keywords:elimination of mean anomaly from Hamiltonian; expansion in powers of eccentricity; classical satellite theories; elimination of parallax; normalization in polar coordinates Citations:Zbl 0508.70008 PDF BibTeX XML Cite \textit{A. Deprit}, Celest. Mech. 26, 9--21 (1982; Zbl 0512.70016) Full Text: DOI OpenURL References: [1] Abraham, R. and Marsden, J. E.: 1978,Foundation of Mechanics, The Benjamin/Cummings Publishing Company, Inc., Reading, Mass. [2] Andoyer, H.: 1913,Bull. Astron. 30, 28. [3] Arnold, V. I.: 1974,Mathematical Methods of Classical Mechanics, translated from Russian by K. Vogtmann and A. Weinstein. Springer-Verlag, New York, Heidelberg, Berlin. [4] Batrakhov, Y. B.: 1960,Bull. Inst. Theor. Astron. (Leningrad)7, 570. [5] Brouwer, D.: 1946,Astron. J. 51, 223. [6] Brouwer, D.: 1958,Astron. J. 63, 433. [7] Brouwer, D.: 1959,Astron. J. 64, 378. [8] Burgoyne, N. and Cushman, R.: 1974,Celest. Mech. 8, 435. · Zbl 0286.34053 [9] Claes, H.: 1980,Celest. Mech. 21, 193. · Zbl 0452.70030 [10] Coffey, S. L. and Deprit, A.: 1980, AIAA Paper 80-1657, AIAA/AAS Astrodynamics Conference. August 1980, Danvers, Mass.,J. Control Guidance,in press. [11] Deprit, A. and Rom A.: 1970,Celest. Mech. 2, 166. · Zbl 0199.60101 [12] Garfinkel, B.: 1958,Astron. J. 63, 88. [13] Herget, P. and Musen, P.: 1958,Astron. J. 63, 430. [14] Hori, G. I.: 1963,Astron. J. 68, 125. [15] Hori, G. I.: 1966,Publ. Astron. Soc. Japan 18, 287. [16] Howland, R. A.: 1979,Celest. Mech. 19, 139. · Zbl 0399.70017 [17] Humphreys, J. E.: 1970,Introduction to Lie Algebras and Representation Theory, Springer-Verlag, New York, Heidelberg, Berlin. · Zbl 0254.17004 [18] Iszak, I.: 1963,Astron. J. 68, 559. [19] Jacobson, N.: 1962,Lie Algebras, Interscience Publishers, New York and London. · Zbl 0121.27504 [20] Jefferys, W. H.: 1971,Celest. Mech. 3, 390. [21] King-Hele, D.: 1958,Proc. Roy. Soc. London A247, 49. · Zbl 0081.17801 [22] Kinoshita, H.: 1977,SAO Special Report No. 379. [23] Kozai, Y.: 1959,Astron. J. 64, 367. [24] Kozai, Y.: 1962,Astron. J. 67, 446. [25] Krause, H. G. L.: 1952, in H. H. Krolle (ed.),Proc. 3rd Int. Astronaut. Congress, Stuttgart, [26] Moshinsky, M.: 1979,Groups in Physics, Séminaire de Mathématiques supèrieures, Département de Mathématiques et de Statistique, Université de Montréal, Les Presses de l’Université de Montréal. [27] Musen, P.: 1959,J. Geophys. Res. 64, 2271. [28] Orlov, A. A.: 1953,Comm. Astron. Inst. Sternberg (Moscow) No. 88-89. [29] Orlov, A. A.: 1954,Mem. Astron. Inst. Sternberg (Moscow)24, 139. [30] Petty, C. M. and Breakwell, J. V.: 1960,J. Franklin Inst. 270, 259. · Zbl 0141.23101 [31] Poincaré, H.: 1886,Bull. Astron. 3, 57. [32] Poincaré, H., 1889,Compt. Rehd. Acad. Sci. Paris 108, 21. [33] Poincaré, H.: 1893,Les Méthodes nouvelles de la mécaniqué céleste, Paris, Gauthier-Villars, Vol.2, Ch. IX. [34] Roberson, R. E.: 1957a,J. Franklin Inst. 264, 181. · Zbl 0151.35302 [35] Roberson, R. E.: 1957b,J. Franklin Inst. 264, 269. [36] Sterne, T. E.: 1958,Astron. J. 63, 28. [37] Struble, R. A.: 1960a,Arch. Rat. Mech. Anal. 7, 87. · Zbl 0173.52004 [38] Struble, R. A.: 1960b,J. Math. Anal. Appl. 1, 300. · Zbl 0098.37402 [39] Tisserand, F.: 1868,J. Math. Pures Appl. 13, 255. [40] Van der Meer, J. C.: 1982,Celest. Mech., in press. [41] Whittaker, E. T.: 1904,A Treatise on the Analytical Dynamics of Particles and Rigid Bodies, Cambridge University Press; also Dover, New York, note on p. 343 and pp. 345?347. [42] Williamson, J.: 1936,Am. J. Math. 58, 141. · Zbl 0013.28401 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.