Abstract
Numerical results have shown that the use of time elements with time transformations provides increased accuracy in the numerical solution of gravitational systems.
To gain additional accuracy improvements, it appears that the time and the time element should be calculated from quantities that have been adjusted so as to satisfy the energy integral exactly.
We also have found that by reducing the growth of the time element to being nearly linear rather than quadratic causes an increase in the magnitude of the local truncation error in the solution but with a decrease in the rate of growth of the truncation error.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Baumgarte, J.: 1972,Celes. Mech. 5, 490.
Baumgarte, J.: 1976,Celes. Mech., this issue, p. 121.
Baumgarte, J. and Stiefel, E.: 1974,Celes. Mech. 10, 71.
Brouwer, D. and Clemence, G.: 1961,Methods of Celestial Mechanics, Academic Press, New York, London.
Nacozy, P.: 1971,Astrophys. Space Sci. 14, 40.
Nacozy, P.: 1974, ‘Time Elements’, in G. Giacaglia (ed.),Satellite Dynamics, Springer-Verlag Publ.
Nacozy, P.: 1976,Celes. Mech. 13, 495.
Stiefel, E. and Scheifele, G.: 1971,Linear and Regular Celestial Mechanics, Springer-Verlag Publ.
Sundman, K. F.: 1912,Acta Math. 36, 105.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Nacozy, P. Numerical aspects of time elements. Celestial Mechanics 14, 129–132 (1976). https://doi.org/10.1007/BF01247139
Issue Date:
DOI: https://doi.org/10.1007/BF01247139