Abstract
Brouwer’s solution to the artificial satellite problem is revisited. We show that the complete Hamiltonian reduction is rather achieved in the plain Poincaré’s style, through a single canonical transformation, than using a sequence of partial reductions based on von Zeipel’s alternative for dealing with perturbed degenerate Hamiltonian systems. Beyond the theoretical interest of the new approach as regards the complete reduction of perturbed Keplerian motion, we also show that a solution based on a single set of corrections may yield computational benefits in the implementation of an analytic orbit propagator.
Highlights
Brouwer’s (1959) analytical solution to the artificial satellite problem based on von Zeipel’s (1965) partial reduction method for dealing with perturbed degenerate Hamiltonians fiercely resists obsolescence sixty years after publication
After the invention of Hamiltonian simplification methods (Deprit 1981), it was suggested that carrying out additional decompositions, increasing the number of canonical transformations, could be the proper way to success in the search for separable perturbation Hamiltonians of celestial mechanics problems (Deprit and Miller 1989)
Soon after Brouwer’s solution appeared in print, different reports pointed out an apparent contradiction between the accuracy expected from the series truncation order and the comparatively large in-track errors obtained in a variety of tests against numerical integrations (Bonavito et al 1969)
Summary
Brouwer’s (1959) analytical solution to the artificial satellite problem based on von Zeipel’s (1965) partial reduction method for dealing with perturbed degenerate Hamiltonians fiercely resists obsolescence sixty years after publication. After the invention of Hamiltonian simplification methods (Deprit 1981), it was suggested that carrying out additional decompositions, increasing the number of canonical transformations, could be the proper way to success in the search for separable perturbation Hamiltonians of celestial mechanics problems (Deprit and Miller 1989).
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