11. Oscillating systems and PLL

It is assumed here that the rapid effects have an oscillating character (see figure 10 ). The averaging method has long been used in celestial mechanics to determine the evolution of planetary orbits under the influence of mutual perturbations between the planets, and to study the stability of the solar system.

Gauss gives the following definition, which is most intuitive: "... the mass of each planet should be distributed along its orbit in proportion to the time spent in each part of the orbit, and the attraction of the planets should be replaced by that of the rings of matter thus defined...".

In this framework, the unperturbed...