Szebehely, V.; Bond, V. Transformations of the perturbed two-body problem to unperturbed harmonic oscillators. (English) Zbl 0516.70013 Celest. Mech. 30, 59-69 (1983). Reviewer: Johannes Viktor Feitzinger (Bochum) Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 2 ReviewsCited in 16 Documents MSC: 70F05 Two-body problems 70-08 Computational methods for problems pertaining to mechanics of particles and systems 70K20 Stability for nonlinear problems in mechanics 70M20 Orbital mechanics Keywords:stability and transformation; perturbed planar problem; unperturbed and undamped harmonic oscillators with constant coefficients; Sundman’s time variable; radial variables; Lyapunov-type stability of isoenergetic manifolds PDFBibTeX XMLCite \textit{V. Szebehely} and \textit{V. Bond}, Celest. Mech. 30, 59--69 (1983; Zbl 0516.70013) Full Text: DOI References: [1] Bond, V. and Janin, G.: 1981,Celes. Mech. 23, 159. · Zbl 0462.70007 · doi:10.1007/BF01229551 [2] Bond, V. and Szebehely, V.: 1982a, ?Transformations of the Two-Body Problem to Harmonic Oscillators,? NASA-JSC-17933, March 1982. [3] Brouwer, D. and Clemence, G.: 1961,Methods of Celestial Mechanics, Academic Press, New York and London. · Zbl 0132.23506 [4] Hagihara, Y.: 1970?1976,Celes. Mech. Vols. 1?5, MIT Press, Cambridge, Massachusetts, and Japan Society for Promotion of Science, Tokyo. [5] Kustaanheimo, P. and Stiefel, E.: 1965,J. reine angewandte Math. 218, 204. [6] Levi-Civita, T.: 1903,Ann. Math. (3) 9, 1. [7] Nacozy, P. E.: 1977,Celes. Mech. 16, 309. · Zbl 0376.70013 · doi:10.1007/BF01232657 [8] Stiefel, E. and Scheifele: 1971,Linear and Regular Celestial Mechanics, Springer Verlag, Berlin and New York. · Zbl 0226.70005 [9] Sundman, K. F.: 1912,Acta. Math. 36, 105. · JFM 43.0826.01 · doi:10.1007/BF02422379 [10] Szebehely, V.: 1967,Theory of Orbits, The Restricted Problem of Three Bodies, Academic Press, New York and London. · Zbl 0202.56902 [11] Szebehely, V. and Bond, V.: 1982b, ?Equations for Autonomous Orbit Calculations?, NASA-JSC-18280, June 1982. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.