Electronic Resource
Springer
Celestial mechanics and dynamical astronomy
10 (1974), S. 497-512
ISSN:
1572-9478
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract The Lie transform method used in Perturbation Theory is based upon an intrinsic algorithm for transforming functions or vector fields by a transformation close to the identity. It can thus be viewed as a specialization of methods and results of differential geometry as is shown in the first part of this paper. In a second part we answer some of the questions left open in connection with the equivalence of the algorithms proposed by Hori and Deprit. From a formal point of view, the methods are shown to be equivalent for non-canonical as well as canonical transformations and a formula relating directly the two generating functions (or vector fields) is presented (formula (5.17)). On the other hand, the equivalence is shown to hold also in the ring ofp-differentiable functions.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01229124
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