Skip to main content
SpringerLink
Log in

The Lissajous transformation IV. Delaunay and Lissajous variables

  • Published:
Celestial Mechanics and Dynamical Astronomy Aims and scope Submit manuscript

Abstract

Relations are established between the Delaunay variables defined over a phase space E in four dimensions and the Lissajous variables defined over a four-dimensional phase space F when the latter is mapped onto E by a parabolic canonical transformation.

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

  • Andoyer, H.: 1913, “Sur l'anoinalie excentrique et l'anomalie vraie comme éléments canoniques du mouvernent elliptique d'apr\es MM. T. Levi-Civita et G.-W. Hill,” Bulletin Astronomique 30, 425–429.

    Google Scholar 

  • Cid, R. and Calvo, M.: 1975, “Sistemas canònicas en mecánica celeste,” Publ. Rev. Acad. Cienc. Zaragoza 30, 43–51.

    Google Scholar 

  • Deprit, A.: 1991, “The Lissajous Transformation I. Basics,” Celest. Mech. 51, 203–226(this issue).

    Google Scholar 

  • Stiefel, E. and Scheifele, G.: 1971, Linear and Regular Celestial Mechanics, Springer-Verlag, New York, Heidelberg, Berlin.

    Google Scholar 

  • Wolfram, S.: 1988, Mathematica. A System for Doing Mathematics by Computer, Addison-Wesley Publishing Company, Inc., Redwood City CA.

    Google Scholar 

Download references

Author information

Author notes

  1. Carol A. Williams

    Present address: Department of Mathematics, University of South Florida, 33620, Tampa, FL

Authors and Affiliations

  1. National Institute of Standards and Technology, 20899, Gaithersburg, MD, U. S. A.

    André Deprit & Carol A. Williams

Authors
  1. André Deprit
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Carol A. Williams
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Deprit, A., Williams, C.A. The Lissajous transformation IV. Delaunay and Lissajous variables. Celestial Mech Dyn Astr 51, 271–280 (1991). https://doi.org/10.1007/BF00051694

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00051694

Key words

Search

Navigation