Abstract
Kamel has recently extended to non-Hamiltonian equations a perturbation theory using Lie transforms. We show here how Kamel's extension can be approached from an intrinsic viewpoint, which reformulation leads to a simpler algorithm. Then we complete Kamel's contribution by establishing the rules for inverting the transformation generated by the perturbation theory, and for composing two such transformations.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Deprit, A.: 1969,Celestial Mech. 1, 12–30.
Deprit, A., Henrard, J., Price, J. F., and Rom, A.: 1969,Celestial Mech. 1, 222.
Gröbner, W.: 1960,Die Lie-Reihen und ihre Anwendungen, Springer, Berlin.
Hori, G.: 1966,Publ. Astron. Soc. Japan 18, 287–296.
Hori, G.: 1967,Publ. Astron. Soc. Japan 19, 229–241.
Kamel, A. A.: 1969a,Celestial Mech. 1, 190–199.
Kamel, A. A.: 1970,Celestial Mech. 3, 90–106.
Poincaré, H.: 1899,Les méthodes nouvelles de la mécanique céleste, Gauthier-Villars, Paris.
Siegel, C. L.: 1941,Ann. Math. 42, 806–828.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Henrard, J. On a perturbation theory using Lie transforms. Celestial Mechanics 3, 107–120 (1970). https://doi.org/10.1007/BF01230436
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01230436