Formation Flight of Earth Satellites on KAM Tori

Kolmogorov, Arnold and Moser (KAM) theory provides that orbits of satellites whose dynamics are representable by an integrable Hamiltonian plus a small, real perturbation lie on tori in phase psace and remin on the KAM tori for all time, unless acted upon by a non-conservative force. A refined technique for constructing KAM tori for Earth-orbiting satellites is developed and implemented using numerically integrated orbital data for hypothetical satellites and involving methods of Fourier analysis and spectral decomposition. Definition of satellite formations on the KAM tori is performed and analyses conducted to investigate both constellations with large seperations and clustors with small separations. Cluster formations with physical secular drift rates on the order of nanometers to micrometers per second are obtained. A brief discussion of effects of non-conservative forces (such as atmospheric drag) on KAM tori is given.