Skip to main content
Log in

Intrinsic variational equations in three dimensions

  • Published:
Celestial mechanics Aims and scope Submit manuscript

Abstract

The variational equations along an orbit in a conservative dynamic system with three degrees of freedom may be separated into (i) a linear system of order four involving only the normal and binormal displacements and (ii) a quadrature to produce the tangential displacement.

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

  • Abraham, R. and Marsden, J. E.: 1978,Foundations of Mechanics, The Benjamin Cummings Publishing Co., London, New York.

    Google Scholar 

  • Birkhoff, G. D.: 1915,Rend. Circ. Mat. Palermo 39, 270.

    Google Scholar 

  • Darwin, G.: 1897,Acta mathematica 21, 99.

    Google Scholar 

  • Deprit, A. and Henrard, J.: 1967,Astron. J. 72, 158.

    Google Scholar 

  • Deprit, A. and Henrard, J.: 1968,Adv. Astron. Astrophys. 6, 1.

    Google Scholar 

  • Hill, G. W.: 1877,The Motion of the Lunar Perigee, Cambridge, Mass., reprinted inActa Math. 8 (1886), 1–36 and then inWorks 1, 243.

  • Korteweg, D. J.: 1886,Sitzungsberichte Math. Nat. Klasse Kaiserl. Akad. Wiss. Wien 93, 995.

    Google Scholar 

  • Message, J. P.: 1959,Astron. J. 64, 226.

    Google Scholar 

  • Poincaré, H.: 1899,Les Méthodes nouvelles de la mécanique céleste, Paris Gauthier-Villars, vol.3, ch. XXIX.

  • Stokes, A.: 1976,Proc. Amer. Math. Soc. 59, 225.

    Google Scholar 

  • Stokes, A.: 1977,J. Diff. Eq. 24, 153.

    Google Scholar 

  • Wintner, A.: 1931,Ber. Sachs. Akad. Wiss. Leipzig 82, 345.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Deprit, A. Intrinsic variational equations in three dimensions. Celestial Mechanics 24, 185–193 (1981). https://doi.org/10.1007/BF01229196

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01229196

Keywords

Navigation