Stabilization and time transformation

Details Stabilization and time transformation Stabilization and time transformation

Mar 1981

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1981acasn..22..328h&link_type=abstract

(Acta Astronomica Sinica, vol. 22, Dec. 1981, p. 328-335.) Chinese Astronomy and Astrophysics, vol. 6, Mar. 1982, p. 37-42. Tra

Mathematics

2

Euler-Lagrange Equation, Numerical Integration, Numerical Stability, Time Functions, Truncation Errors, Two Body Problem, Independent Variables, Liapunov Functions, Orbital Mechanics, Periodic Functions, Transformations (Mathematics)

Scientific paper

A simple stabilization technique to reduce the along-track error in the numerical integration of the Lagrange's equations of motion is suggested. The equations of motion of the two-body problem are investigated after applying a Sundman transformation both with and without introducing the energy integral. In both cases, how the stability of the equations varies with alpha is shown and, in the case with the energy integral, it is demonstrated that every solution is a quasi-periodic function of the independent variable s with two frequencies.

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