Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-13T05:29:12.585Z Has data issue: false hasContentIssue false
  • English
  • Français

On two-parameter linearizing transformations for uniform treatment of two-body motion

Published online by Cambridge University Press:  25 May 2016

Luis Floría
Luis Floría*
Affiliation:
GMC, Departamento de Matemática Aplicada a la Ingeniería, E.T.S. de Ingenieros Industriales, Universidad de Valladolid, E-47 011 Valladolid, Spain

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Differential changes of time involving two parameters are considered. Universal expressions for dynamical variables of interest in Keplerian motion allow us to reduce the integration of the time transformations to that of integrands depending on an eccentric-like universal anomaly. Elliptic integrals and functions are required to complete the integration.

Keywords

reparametrizing transformationsgeneralized anomaliesuniform treatment of Keplerian systemsuniversal functionselliptic functions
Type
Part VII - The Calculus of Perturbations
Information
Symposium - International Astronomical Union , Volume 172: Dynamics, Ephemerides and Astrometry of the Solar System , 1996 , pp. 299 - 302
Copyright
Copyright © Kluwer 1996 

References

Battin, R. H. (1987) An Introduction to the Mathematics and Methods of Astrodynamics. American Institute of Aeronautics and Astronautics Education Series, New York.Google Scholar
Belen'kii, I. M. (1981) A Method of Regularizing the Equations of Motion in the Central Force-Field, Celestial Mechanics 23, 9–32.CrossRefGoogle Scholar
Brumberg, E. V. (1992) Length of Arc as Independent Argument for Highly Eccentric Orbits, Celestial Mechanics and Dynamical Astronomy 53, 323–328.CrossRefGoogle Scholar
Cid, R., Ferrer, S. and Elipe, A. (1983) Regularization and Linearization of the Equations of Motion in Central Force-Fields, Celestial Mechanics 31, 73–80.CrossRefGoogle Scholar
Ferrándiz, J. M. and Ferrer, S. (1986) A New Integrated, General Time Transformation in the Kepler Problem, Bulletin of the Astronomical Institutes of Czechoslovakia 37, 226–229.Google Scholar
Ferrándiz, J. M., Ferrer, S. and Sein-Echaluce, M. L. (1987) Generalized Elliptic Anomalies, Celestial Mechanics 40, 315–328.CrossRefGoogle Scholar
Stiefel, E. L. and Scheifele, G. (1971) Linear and Regular Celestial Mechanics. Springer-Verlag, Berlin, Heidelberg, New York.CrossRefGoogle Scholar
Stumpff, K. (1959) Himmelsmechanik, I. VEB Deutscher Verlag der Wissenschaften, Berlin.Google Scholar