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Theory compression with elliptic functions

Published online by Cambridge University Press:  25 May 2016

Victor A. Brumberg
Victor A. Brumberg*
Affiliation:
Bureau des Longitudes 77, av. Denfert-Rochereau, Paris 75014, France (On leave from Institute of Applied Astronomy 8, Zhdanovskaya st., St.-Petersburg 197042, Russia)

Abstract

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Introduction of Jacobi elliptic functions in planetary, satellite and cometary problems of celestial mechanics is a transformation of variables to present the analytical theories of motion in the more compact form as compared with the traditional series in multiples of mean longitudes or mean anomalies.

Type
Part II - Planets and Moon: Theory and Ephemerides
Information
Symposium - International Astronomical Union , Volume 172: Dynamics, Ephemerides and Astrometry of the Solar System , 1996 , pp. 89 - 100
Copyright
Copyright © Kluwer 1996 

References

Boda, K.: 1931, ‘Entwicklung der Störungsfunction und ihrer Ableitungen in Reihen, welche für beliebige Exzentrizitäten und Neigungen konvergieren’, Astron. Nachr., 243, 17 CrossRefGoogle Scholar
Bond, V.R. and Janin, G.: 1981, ‘Canonical Orbital Elements in Terms of an Arbitrary Independent Variable’, Celes. Mech. 23, 159 Google Scholar
Bretagnon, P.: 1982, ‘Théorie du mouvement de l'ensemble des planétes. Solution VSOP82’, Astron. Astrophys. 114, 278 Google Scholar
Brown, E.W. and Shook, C.A.: 1933, Planetary Theory, Cambridge Univ. Press Google Scholar
Brumberg, E.: 1992, ‘Perturbed Two-Body Motion with Elliptic Functions’, Proc. 25th Symposium on Celestial Mechanics (eds. Kinoshita, H. and Nakai, N.), 139, NAO, Tokyo Google Scholar
Brumberg, E.: 1995, ‘Elliptic Anomaly Expansions to Construct High-Eccentricity Satellite Theory’, Abstract 6a3, IAU Symposium No. 172, Paris Google Scholar
Brumberg, E. and Fukushima, T.: 1994, ‘Expansions of Elliptic Motion Based on Elliptic Function Theory’, Celes. Mech. 60, 69 Google Scholar
Brumberg, E., Brumberg, V.A., Konrad, Th. and Soffel, M.: 1995, ‘Analytical Linear Perturbation Theory for Highly Eccentric Satellite Orbits’, Celes. Mech. 61, 369 Google Scholar
Brumberg, V.A.: 1995, Analytical Techniques of Celestial Mechanics, Springer Google Scholar
Brumberg, V.A. and Klioner, S.A.: 1995, ‘Intermediate Orbit for General Planetary Theory in Elliptic Functions’, Abstract A16, IAU Symposium No. 172, Paris Google Scholar
Chapront, J. and Chapront-Touzé, M.: 1995, ‘Comparaison de la théorie du mouvement de la Lune ELP aux observations: la boite à outils’, Notes sci. et techn. du BDL S050, 105 Google Scholar
Chapront, J. and Simon, J. L.: 1988, ‘Perturbations du premier ordre pour des couples de planètes’, Bureau des Longitudes (unpublished) Google Scholar
Howland, R.A.: 1988, ‘A New Approach to the Librational Solution in the Ideal Resonance Problem’, Celes. Mech. 44, 209 CrossRefGoogle Scholar
Kinoshita, H. and Souchay, J.: 1990, ‘The Theory of the Nutation for the Rigid Earth Model at the Second Order’, Celes. Mech. 48, 187 Google Scholar
Laskar, J. and Robutel, Ph.: 1995, ‘Stability of the Planetary Three-Body Problem. I. Expansion of the Planetary Hamiltonian. Celes. Mech. (in press) Google Scholar
Nacozy, P.: 1969, ‘Hansen's Method of Partial Anomalies: An Application’, Astron. J. 74, 544 Google Scholar
Nacozy, P.: 1977, ‘The Intermediate Anomaly’, Celes. Mech. 16, 309 Google Scholar
Osácar, C. and Palacián, J.: 1994, ‘Decomposition of Functions for Elliptic Orbits’, Celes. Mech. 60, 207 Google Scholar
Petrovskaya, M.S.: 1970, ‘Expansions of the Negative Powers of Mutual Distance Between Bodies’, Celes. Mech. 3, 121 Google Scholar
Petrovskaya, M.S.: 1972, ‘Expansions of the Derivatives of the Disturbing Function in Planetary Problems’, Celes. Mech. 6, 328 CrossRefGoogle Scholar
Richardson, D.L.: 1982, ‘A Third-Order Intermediate Orbit for Planetary Theory’, Celes. Mech. 26, 187 CrossRefGoogle Scholar
Skripnichenko, V.I.: 1972, ‘On the Application of Hansen's Method of Partial Anomalies to the Calculation of Perturbations in Cometary Motions’, in Chebotarev, G. A., Kazimirchak-Polonskaya, E.I., and Marsden, B. G. (eds.), The Motion, Evolution of Orbits, and Origin of Comets, p. 52, Reidel, Dordrecht CrossRefGoogle Scholar
Williams, C.A., Van Flandern, T., and Wright, E.A.: 1987, ‘First Order Planetary Perturbations with Elliptic Functions’, Celes. Mech. 40, 367 CrossRefGoogle Scholar
Yuasa, M. and Hori, G.: 1979, ‘New Approach to the Planetary Theory’, in Duncombe, R. L. (ed.), Dynamics of the Solar System, p. 69, Reidel, Dordrecht Google Scholar
Zeipel, H.: 1912, ‘Entwicklung der Störungsfunktion’, Encyklopädie der math. Wiss. 6 (2), 557 Google Scholar