Effects of Air Drag and Lunar Third-Body Perturbations on Orbital Motion Near a Reference Kam Torus

The KAM Theory was developed in the 1960s but only in the last decade has it been applied to Earth orbiting satellites. Physical state variables of position and velocity are transformed into KAM Torus variables. The KAM Torus is a geometrical structure similar to that of a multi-dimensional donut. The Earth satellite's motion can be described as traversing the surface of this donut. There are two primary advantages of this transformation: (1) The new generalized coordinates which are analogous with mean anomaly, right ascension of the ascending node, and argument of perigee, increment linearly with time, and (2) Perturbations due to the Earth's geopotential are already embedded in a given torus to an arbitrary geopotential order. This study examines methods to describe perturbed satellite motion near a reference KAM Torus.