Abstract
A new technique is developed for the formal solution of non-degenerate or degenerate Hamiltonian systems under periodic perturbation through continually accelerated elimination of the periodic terms. Special features of the method are the ability to eliminate both short-period and longperiod variables simultaneously and the attainment of [formal] ‘quadratic convergence’ for non-degenerate systems and nearly quadratic convergence in degenerate cases. The technique utilizes Lie transforms and is based on an approach due to Kolmogorov and Arnol'd.
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Howland, R.A. An accelerated elimination technique for the solution of perturbed Hamiltonian systems. Celestial Mechanics 15, 327–352 (1977). https://doi.org/10.1007/BF01228426
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DOI: https://doi.org/10.1007/BF01228426