Strongly perturbed quasi-periodic dynamical systems

It is almost impossible to construct a general theory of the motion of a strongly perturbed dynamical system using classical perturbation theory because this approach uses a reference orbit (e.g. a Keplerian ellipse) which is very different from the actual orbit.A general method, pioneered by Jefferys, is presented here. This method allows each quasi-periodic orbit (for instance a strongly perturbed two body problem: JVIII is the typical example) to specify the coordinates to be used. These coordinates are discovered by a truncated infinite series of coordinate transformations. The transformations are implemented using the idea that the nature of a dynamical system is embodied in the symplectic form. The method is illustracted by a simple example.With modern algebraic and series manipulation languages on present day computers all one needs to begin using this approach is a good numerical integration, the end product being a series for each coordinate. Further weak perturbations are easily incorporated into this semi-analytical solution by the usual methods.Proceedings of the Conference on Analytical Methods and Ephemerides: Theory and Observations of the Moon and Planets. Facultés universitaires Notre Dame de la Paix, Namur, Belgium, 28–31 July, 1980.