Skip to main content
SpringerLink
Log in

Towards a rigorous justification of the Stiefel-Baumgarte stabilization method

  • Published:
Celestial mechanics Aims and scope Submit manuscript

Abstract

The purpose of the present paper is to continue the work on the mathematical justification of the Baumgarte dissipative stabilization procedure. Using ideas reminiscent of the theory of invariant manifolds, geometrical results and error bounds are obtained.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Arnold, V. I.: 1976,Méthodes Mathématiques de la Mécanique Classique.

  • Baumgarte, J.: 1972a,Celest. Mech. 5, 490.

    Google Scholar 

  • Baumgarte, J.: 1972b,Comp. Meth. in Appl. Mech. and Eng. 1, 1.

    Google Scholar 

  • Baumgarte, J.: 1973a,ZAMM 53, 44.

    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.

  • Baumgarte, J.: 1973c,Celest. Mech. 8, 223.

    Google Scholar 

  • Baumgarte, J.: 1973d,ZAMM 53, 701.

    Google Scholar 

  • Baumgarte, J.: 1976a, ‘Stabilization, Manipulation and Analytic Step Adaption’, in V. Szebehely and B. D. Tapley (eds.),Long-Time Predictions in Dynamics.

  • Baumgarte, J.: 1976b,Celest. Mech. 13, 247.

    Google Scholar 

  • Baumgarte, J. and Stiefel, E.: 1974a, ‘Examples of Transformations Improving the Numerical Accuracy of the Integration of Differential Equations’, Lecture Notes 362, 207.

  • Baumgarte, J. and Stiefel, E.: 1974b,Celest. Mech. 10, 71.

    Google Scholar 

  • Hartman, P.: 1964,Ordinary Differential Equations.

  • Hochfeld, E. (ed): 1957,Stabilization of Computer Circuits, Univ. of Chicago.

  • Kirchgraber, U.: 1978,C. R. Acad. Sci. 286, 421.

    Google Scholar 

  • Kirchgraber, U.: 1979,ZAMP 30, 272.

    Google Scholar 

  • Kirchgraber, U. and Stiefel, E.: 1978,Methoden d. Analytischen Stoerungsrechnung.

  • Knobloch, H. W. and Kappel, F.: 1974,Gewoehnliche Differentialgleichungen.

  • Marsden, J. and McCracken, M.: 1976,The Hopf Bifurcation and its Applications.

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

    Google Scholar 

  • Schwarz, R.: 1972,Comp. Meth. in Appl. Mech. and Eng.,1, 279.

    Google Scholar 

  • Sigrist, N.: 1974,ZAMP 25, 37.

    Google Scholar 

  • Stokes, A.: 1975,Mech. Res. Comm. 2, 267.

    Google Scholar 

  • Stokes, A.: 1978,SIAM J. Appl. Math. 35, 564.

    Google Scholar 

  • Zubov, V. I.: 1976,Diff. Eqn. 11, 1685.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Lefschetz Center for Dynamical Systems, Brown University, 02912, Providence, R.I., USA

    Urs Kirchgraber

Authors
  1. Urs Kirchgraber
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Proceedings of the Sixth Conference on Mathematical Methods in Celestial Mechanics held at Oberwolfach (West Germany) from 14 to 19 August, 1978.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kirchgraber, U. Towards a rigorous justification of the Stiefel-Baumgarte stabilization method. Celestial Mechanics 21, 225–236 (1980). https://doi.org/10.1007/BF01230901

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01230901

Keywords

Search

Navigation