THE USE OF MODIFIED HILL’S VARIABLES IN THE METHOD OF AVERAGING

Boronenko Tatyana Stepanovna

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In this paper the modified Hill’s canonical variables are introduced. They are v, G, H; r, g, h, where r is the distance to the primary for Keplerian orbit ; v = dr / dt; G= aј(1e2) and H = G cos i are Delaunay’s variables; g = Й is the argument of the periapsis; h = © is the longitude of the ascending node. We show that the modified Hill’s canonical variables are useful in some analytical theories of motion where it is need to avoid expansion of the perturbations in powers of eccentricity and where it is advantageous to use the eccentric anomaly as independent variable. As an example, we consider the single-averaged analytical model in the frame of the restricted three-body problem for satellite case.

Keywords: небесная механика, теория возмущений, метод усреднения, преобразования Ли, канонические переменные Хилла, ограниченная задача трех тел, динамика спутников планет

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Issue: 8, 2011

Series of issue: Issue 8

Pages: 53 — 56

Downloads: 885