Celestial mechanics

, Volume 1, Issue 1, pp 110–126 | Cite as

Perturbations in rectangular coordinates by iteration

  • R. Broucke


An investigation has been made on computing orbits with Picard's method of successive approximations. The perturbations are integrated in the form of a general displacement from a fixed Keplerian reference orbit. Several variation-of-parameters methods are obtained for the integration of the displacement equation. These variation-of-parameters methods could be used as special perturbation or general perturbation methods. The present paper investigates the applications as iterative numerical perturbation techniques. Four different formulations are proposed. They have been implemented on a computer with Chebychev series and their respective advantages and disadvantages are analyzed. Connections with other known perturbation methods are also described.


Perturbation Method Successive Approximation Perturbation Technique General Displacement General Perturbation 
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Copyright information

© D. Reidel Publishing Company 1969

Authors and Affiliations

  • R. Broucke
    • 1
  1. 1.Jet Propulsion LaboratoryCalifornia Institute of TechnologyPasadenaUSA

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