Application of Hori technique in general planetory theory. I: First step
type: Item
instance of: scholarly article
title: Application of Hori technique in general planetory theory. I: First step
zbMATH Open document ID: 0668.70016
DOI: 10.1007/BF00054243
author: Osman M. Kamel
published in: Earth, Moon, and Planets
publication date: 1989-01-01T00:00:00Z
review text: We explain how the first step of Hori-Lie procedure is applied in general planetory theory to eliminate short-period terms. We extend the investigation to the third-order planetary theory. We solved the canonical equations of motion for secular and periodic perturbations by this method, and obtained the first integrals of the system of canonical equations. Also we showed the relation between the determining function in the sense of Hori and the determining function in the sense of Von Zeipel.
Mathematics Subject Classification ID: 70F15
zbMATH DE Number: 4094897
zbMATH Keywords: Hori-Lie procedure
zbMATH Keywords: planetory theory
zbMATH Keywords: short-period terms
zbMATH Keywords: third-order planetary theory
zbMATH Keywords: periodic perturbations
zbMATH Keywords: canonical equations
MaRDI profile type: Publication
cites work: Invariance in Von Zeipel method
cites work: Equivalence of the perturbation theories of Hori and Deprit
cites work: Canonical transformations depending on a small parameter
cites work: A new algorithm for the Lie transformation
cites work: Explicit recursive algorithms for the construction of equivalent canonical transformations
cites work: On the elimination of short-period terms in second-order general planetary theory investigated by Hori's method
cites work: On the elimination of the critical terms of a first order theory of Jupiter perturbed by Saturn carried out through Hori's method and Poincar� canonical variables
full work available at URL: https://doi.org/10.1007/bf00054243
OpenAlex ID: W1527716705
description: scientific article; zbMATH DE number 4094897