Skip to main content
Log in

A new time element for a general time transformation

  • Published:
Celestial mechanics Aims and scope Submit manuscript

Abstract

The paper introduces a new time element to be used with a general time transformation for satellite equations of motion. The purpose of this time element is to reduce the growth of the numerical errors with respect to the time integration. It is characteristic for the new time element τ, that the relation between the timet and the element τ does not depend on the independent variables.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Baumgarte, J.: 1972a,Celes. Mech. 5, 490–501.

    Google Scholar 

  • Baumgarte, J.: 1972b,Comp. Methods Appl. Mech. Eng. 1, 1–16.

    Google Scholar 

  • Baumgarte, J.: 1973a,J. Appl. Math. Mech. (ZAMM) 53, 701–704.

    Google Scholar 

  • Baumgarte, J.: 1973b, ‘Stabilization of the Differential Equations of Keplerian Motion’, in B. D. Tapley and V. Szebehely (eds.),Recent Advances in Dynamical Astronomy, D. Reidel Publ. Co., pp. 38–44.

  • Baumgarte, J.: 1975a, ‘Stabilized Kepler Motion Connected with Analytic Step Adaption’, to appear inCeles. Mech.

  • Baumgarte, J.: 1975b, ‘Stabilization, manipulation and analytic step adaption’, to appear in the Proceedings of the NATO Advanced Study Institut.

  • Baumgarte, J. and Stiefel, E.: 1974a, ‘Examples of Transformations Improving the Numerical Accuracy of the Integration of Differential Equations’, in D. G. Bettis (ed.),Lecture Notes in Mathematics, Vol. 362, 207–236.

  • Baumgarte, J. and Stiefel, E.: 1974b,Celes. Mech. 10, 71–85.

    Google Scholar 

  • Beaudet, P. R.: 1974, ‘Dynamic Stabilization and Error Propagation in Perturbed Keplerian Motion’, Prepared by Computer Sciences Corporation for Goddard Space Flight Center, Contact No. NAS 11 999, Task. Assignment No. 086.

  • Hochfeld, E. (ed.): 1957, ‘Stabilization of Computer Circuits’, Univ. of Chicago, Available from US Govt., Printing Office, Washington D.C., as WADC TR 57-425 (AD 155740).

    Google Scholar 

  • Nacozy, P. E.: 1971,Astrophys. Space Sci. 14, 40–51.

    Google Scholar 

  • Nacozy, P. E.: 1972, Studies performed at The University of Texas at Austin.

  • Nacozy, P. E.: 1973,Bull. Am. Astron. Soc. 5, No. 1.

    Google Scholar 

  • Sigrist, N.:J. Appl. Math. Phys. (ZAMP) 25, 37–46.

  • Stiefel, E. L. and Scheifele, G.: 1971,Linear and Regular Celestial Mechanics, Springer Verlag.

  • Velez, C. E.: 1974,Celes. Mech. 10, 405–422.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Baumgarte, J. A new time element for a general time transformation. Celestial Mechanics 14, 121–127 (1976). https://doi.org/10.1007/BF01247138

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01247138

Keywords

Navigation