An accelerated elimination technique for the solution of perturbed Hamiltonian systems

Details An accelerated elimination technique for the solution of perturbed Hamiltonian systems An accelerated elimination technique for the solution of perturbed Hamiltonian systems

Apr 1977

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1977cemec..15..327h&link_type=abstract

Celestial Mechanics, vol. 15, Apr. 1977, p. 327-352.

Mathematics

10

Convergence, Elimination, Hamiltonian Functions, Periodic Functions, Perturbation Theory, Acceleration, Canonical Forms, Equations Of Motion, Kolmogoroff Theory, Transformations (Mathematics)

Scientific paper

A new technique is developed for the formal solution of nondegenerate 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 long-period variables simultaneously and the attainment of (formal) 'quadratic convergence' for nondegenerate 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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