The History of the Theory of Averaging

Abstract

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 such as the Moon in the case of the Earth, the interaction of large planets such as 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.