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A Note on the Regularization of the Restricted Three‐body Problem
Author(s) -
Leimanis E.
Publication year - 1976
Publication title -
astronomische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.394
H-Index - 63
eISSN - 1521-3994
pISSN - 0004-6337
DOI - 10.1002/asna.19762970306
Subject(s) - regularization (linguistics) , equations of motion , schwarzschild radius , transformation (genetics) , motion (physics) , power series , mathematics , mathematical analysis , series (stratigraphy) , physics , classical mechanics , gravitation , computer science , paleontology , biochemistry , chemistry , biology , gene , artificial intelligence
The requirement that near a singular point of the equations of motion the power series expansions of the old variables in terms of the new ones start with second order terms leads to the transformation z = sin 2 1/2 w related to that of THIELE ‐ BURRAU . Using this new transformation, a derivation of the regularized equations of motion is given. The original as well as the regularized equations of motion are of interest, for example, for calculating the initial values of the orbital elements for SCHWARZSCHILD's periodic solutions ( LEIMANIS and OLUND 1972).