A computer aided analysis of the Sitnikov problem
type: Item
instance of: scholarly article
title: A computer aided analysis of the Sitnikov problem
zbMATH Open document ID: 0780.70005
DOI: 10.1007/BF00699722
author: Johannes Hagel
author: Thomas Trenkler
published in: Celestial Mechanics and Dynamical Astronomy
publication date: 1994-01-30T00:00:00Z
review text: We deal with the problem of a zero mass body oscillating perpendicular to a plane in which two heavy bodies of equal mass orbit each other on Keplerian ellipses. The zero mass body intersects the primaries plane at the systems barycenter. This problem is commonly known as the Sitnikov problem. In this work we are looking for a first integral related to the oscillatory motion of the zero mass body. This is done by expressing the equation of motion by a second order polynomial differential equation using a Chebyshev approximation techniques. We search for an autonomous mapping of the canonical variables over one period of the primaries. In addition, we present a detailed analysis of the linearized Sitnikov problem which is valid for infinitesimally small oscillation amplitudes of the zero mass body. All computations are performed automatically by the FORTRAN program SALOME which has been designed for stability considerations in high energy particle accelerators.
Mathematics Subject Classification ID: 70F07
Mathematics Subject Classification ID: 70-08
zbMATH DE Number: 429318
zbMATH Keywords: perturbation theory
zbMATH Keywords: symplectic mapping
zbMATH Keywords: zero mass body
zbMATH Keywords: first integral
zbMATH Keywords: second order polynomial differential equation
zbMATH Keywords: Chebyshev approximation techniques
zbMATH Keywords: autonomous mapping
zbMATH Keywords: FORTRAN program SALOME
MaRDI profile type: Publication
cites work: A new analytic approach to the Sitnikov problem
cites work: Regular and stochastic motion
cites work: Stable and Random Motions in Dynamical Systems
cites work: Q3844116
cites work: On the Sitnikov problem
full work available at URL: https://doi.org/10.1007/bf00699722
OpenAlex ID: W4229500087
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description: scientific article; zbMATH DE number 429318