Strongly perturbed quasi-periodic dynamical systems

Details Strongly perturbed quasi-periodic dynamical systems Strongly perturbed quasi-periodic dynamical systems

Jan 1982

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1982cemec..26...41s&link_type=abstract

(Conference on Analytical Methods and Ephemerides: Theory and Observations of the Moon and Planets, Namur, Belgium, July 28-31,

Physics

Coordinate Transformations, Dynamic Models, Equations Of Motion, Orbit Perturbation, Orbital Mechanics, Perturbation Theory, Degrees Of Freedom, Hamiltonian Functions, Numerical Integration, Periodic Functions, Toruses

Scientific paper

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 which is very different from the actual orbit. A general method, pioneered by Jefferys (1968, 1976), is presented. This method allows each quasi-periodic orbit 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 illustrated by a simple example. Further weak perturbations are easily incorporated into this semi-analytical solution by the usual methods.

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