Skip to main content Accessibility help
×
Home

Stabilization by Making Use of a Generalized Hamiltonian Variational Formalism

  • Joachim W. Baumgarte (a1)

Abstract

A generalized Hamiltonian formalism is established which is invariant not only under canonical transformations but under arbitrary transformations. Moreover the dependent variables, coordinates and momenta, as well as the independent variable are allowed to be transformed. This is to say that instead of the physical time t another independent variable s is used, such that t becomes a dependent variable or, more precisely, an additional coordinate. The formalism under consideration permits also to include nonconservative forces.

In case of Keplerian motion we propose to use the eccentric anomaly as the independent variable. By virtue of our generalized point of view a Lyapunov-stable differential system is obtained, such that all coordinates, including the time t, are computed by stable procedures. This stabilization is performed by control terms. As a new result a stabilizing control term also for the time integration is established, such that no longer any kind of time element is needed. This holds true for the usual coordinates as well as for the KS-coordinates.

    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Stabilization by Making Use of a Generalized Hamiltonian Variational Formalism
      Available formats
      ×

      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      Stabilization by Making Use of a Generalized Hamiltonian Variational Formalism
      Available formats
      ×

      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      Stabilization by Making Use of a Generalized Hamiltonian Variational Formalism
      Available formats
      ×

Copyright

References

Hide All
1. Baumgarte, J.: Numerical Stabilization of the Differential Equations of Keplerian Motion, Celes. Meen. 5, 490501, (1972).
2. Baumgarte, J.: Stabilization by Modification of the Lagrangian, Celes. Mech. 13, 247251, (1976).
3. Baumgarte, J.: Stabilization, Manipulation and Analytic Step Adaption, Long-Time Predictions in Dynamics, edited by Szebehely, V. and Tapley, B. D., Nato Advanced Study Institutes Series, Series C -Mathematical and Physical Sciences, Vol. 26, D. Reidel Publishing Company, Dordrecht-Holland/Bostǫn-U.S.A., (1976).
4. Stiefel, E.L. and Scheifele, G.: Linear and Regular Celestial mechanics, Springer, Berlin-Heidelberg-New York, (1971).

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed