A general algorithm for the determination of Tj(n) and Zj-asterisk(n) in Hori's method for non-canonical systems

Details A general algorithm for the determination of Tj(n) and Zj-asterisk(n) in Hori's method for non-canonical systems A general algorithm for the determination of Tj(n) and Zj-asterisk(n) in Hori's method for non-canonical systems

Oct 1983

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1983cemec..31..109s&link_type=abstract

Celestial Mechanics (ISSN 0008-8714), vol. 31, Oct. 1983, p. 109-113. Research supported by the Financiadora de Estudos e Projet

Mathematics

2

Celestial Mechanics, Differential Equations, Equations Of Motion, Linear Equations, Secular Variations, Transformations (Mathematics), Algorithms, Matrices (Mathematics), Nonlinear Equations, Oscillations

Scientific paper

A general algorithm is deduced for the determination of Tj(n) and Zj-asterisk(n). It derives from the general solution to nonhomogeneous linear differential equations with variable coefficients in their matrix form. This is achieved by introducing a new function, X-asterisk(n), which is associated with Z-asterisk(n). It then becomes possible to calculate Z-asterisk(n) in such a way that it contains secular or mixed secular terms and T(n) is free of these terms.

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