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Simplifications toward integrability of perturbed Keplerian systems. (English) Zbl 0734.70008

Integrability in dynamical systems, Pap. 3rd Fla. Workshop Nonlinear Astron., Gainesville/FL (USA) 1987, Ann. N. Y. Acad. Sci. 536, 127-139 (1988).
[For the entire collection see Zbl 0718.00013.]
Generally spoken perturbed Keplerian systems are non-integrable. The task of analyzing the structural reasons for non-integrability may be considerably simplified by using appropriate coordinates. This is one motive for the need of coordinate transformations rather vaguely defined as normalizations or simplifications. Another motive is the still enduring gap between accuracy of measurement and of numerical integration e.g. in lunar theory. After discussing the most illustrative examples for simplification, lunar theory and artificial satellite theory, the authors give a general definition of simplification in terms of Poisson algebra theory. The notion of a radial simplification is also introduced.

MSC:

70F15 Celestial mechanics
70H15 Canonical and symplectic transformations for problems in Hamiltonian and Lagrangian mechanics

Citations:

Zbl 0718.00013