Elliptic Anomaly in Constructing Long-Term and Short-Term Dynamical Theories

Authors: Brumberg, V.A.; Brumberg, E.V.

Source: Celestial Mechanics and Dynamical Astronomy, Volume 80, Numbers 3-4, July 2001 , pp. 159-166(8)

Publisher: Springer

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Abstract:

The techniques of Brumberg and Brumberg (1999) based on the use of elliptic anomaly are specified in this paper in two aspects. The iteration technique (Broucke, 1969) to construct short-term semi-analytical theories of motion in rectangular coordinates in lines of Encke and Hill is reelaborated in terms of elliptic anomaly resulting in extending this technique for high-eccentricity orbits. In constructing long-term semi-analytical theories the key point is to integrate trigonometric functions of several angular arguments related to time by different differential expressions. This problem is reduced in the paper to linear algebraic recurrence relations admitting efficient solution by iterations.

Keywords: elliptic anomaly; iteration techniques; trigonometric series integration

Document Type: Regular Paper

Affiliations: Institute of Applied Astronomy, 197042 St. Petersburg, Russia

Publication date: July 1, 2001

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