Second-order solution of Lindstedt's equation with constant coefficients

Details Second-order solution of Lindstedt's equation with constant coefficients Second-order solution of Lindstedt's equation with constant coefficients

Mar 1982

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1982cha%26a...6....5t&link_type=abstract

Chinese Astronomy and Astrophysics, Volume 6, Issue 1, p. 5-12.

Astronomy and Astrophysics

Astrophysics

Scientific paper

The Hori-Lie transformation for a non-conservative system is applied to the Lindstedt's equation with constant coefficients. A second-order solution when the right hand is a quartic polynomial is derived explicity. We made two applications of our solution. We obtained a new form of the trajectorv of a test particle moving in a Schwarzschild field. The radius of the particle is a periodic funciton of the polar angle with a period slightly different from 2π. The deviation is the relativistic precession. We also considered the solution of the coordinates ρ and η in Vinti's problem containing J3. They are expressed as periodic functions of O'Mathuna's regularization argument.

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