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Originally Posted by grant hutchison
Objects can librate periodically around a 2:1 mean-motion resonance, swinging through a range of values of a and e. This is much more common in the wild, I understand, than an exact, unchanging resonance. Again, the author may be showing you mean values over a longer time period.
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Oh, and you're probably aware that 2:1 resonances can be either stable or unstable, depending on the relative orientations of the orbits, and relative positions of the planets. Is it possible you're setting up an unstable resonance as your starting point?
Grant Hutchison