Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-25T02:00:49.010Z Has data issue: false hasContentIssue false
  • English
  • Français

Planetary equations in terms of vectorial elements

Published online by Cambridge University Press:  24 October 2008

R. R. Allan  and
G. N. Ward
R. R. Allan
Affiliation:
Royal Aircraft Establishment, Farnborough and The College of Aeronautics, Cranfield
G. N. Ward
Affiliation:
Royal Aircraft Establishment, Farnborough and The College of Aeronautics, Cranfield
Get access Rights & Permissions [Opens in a new window]

Abstract

The planetary equations for natural elements, which do not depend upon the choice of a particular frame of reference, are derived by using the theory of Poisson brackets. These natural elements include vectorial elements which lead to the introduction of vector and dyadic Poisson brackets. The use of vectorial elements can also lead to redundancy in the set of elements; this idea is extended to show that as many redundant elements as desired can be used and that the evaluation of the derivatives of the disturbing function can be simplified thereby.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 59 , Issue 3 , July 1963 , pp. 669 - 677
Copyright
Copyright © Cambridge Philosophical Society 1963

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Milankovitch, M., Ueber die Verwendung vectorieller Bahnelemente in der Störungsrechnung. Acad. Serbe. Bull. Acad. Sci. Mat. Nat. A, no. 6 (Belgrade, 1939).Google Scholar
(2)Musen, P., On the long-period lunar and solar effects on the motion of an artificial satellite, 2. J. Geophys. Res. 66 (1961), 2797–2805.CrossRefGoogle Scholar
(3)Goldstein, H., Classical mechanics, chap. 8 (Addison-Wesley; Reading, Mass., 1959).Google Scholar