Abstract

The critical inclination problem in artificial satellite theory, first “discovered” 30 years ago, has aroused great interest and provoked much discussion and controversy in the intervening years. It was this problem which essentially provided the seed corn for the development of the theory of the Ideal Resonance Problem (IRP). The latter theory provides good first-approximation solutions to a number of important resonance problems in celestial mechanics. It is not applicable, however, to certain other interesting resonant systems within the solar system. For these resonances a new “fundamental” mathematical model of resonance, in the spirit of the IRP, has recently been formulated and successfully applied.

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