• Jan A. Sanders
  • Ferdinand Verhulst
Part of the Applied Mathematical Sciences book series (AMS, volume 59)


Perturbation methods for differential equations became important when scientists in the 18th century were trying to relate Newton’s theory of gravitation to the observations of the motion of planets and satellites. Right from the beginning it became clear that a dynamical theory of the solar system based on a superposition of only two-body motions, one body being always the sun and the other body being formed by the respective planets, produces a reasonable but not very accurate fit to the observations. To explain the deviations one considered effects as the influence of satellites like the moon in the case of the earth, the interaction of large planets like Jupiter and Saturn, the resistance of the ether and other effects. These considerations led to the formulation of perturbed two-body motion and, as exact solutions were clearly not available, the development of perturbation theory.


Cotangent Bundle Celestial Mechanic Secular Equation High Order Approximation Kepler Problem 
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Copyright information

© Springer Science+Business Media New York 1985

Authors and Affiliations

  • Jan A. Sanders
    • 1
  • Ferdinand Verhulst
    • 2
  1. 1.Department of Mathematics and Computer ScienceFree UniversityAmsterdamThe Netherlands
  2. 2.Mathematical InstituteState University of UtrechtUtrechtThe Netherlands

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