In canonical von Zeipel perturbation theory, second-order back-substitution can generate a secular, long-timescale change in the semi-major axis, as shown in a toy model.
Mathematical methods of classical mechanics
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On the secular evolution of the semi-major axis in canonical formalism
In canonical von Zeipel perturbation theory, second-order back-substitution can generate a secular, long-timescale change in the semi-major axis, as shown in a toy model.