On the solving of the Hill's differential equation through the method of operational calculus

Details On the solving of the Hill's differential equation through the method of operational calculus On the solving of the Hill's differential equation through the method of operational calculus

Aug 1980

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1980m%26p....23...73m&link_type=abstract

Moon and the Planets, vol. 23, Aug. 1980, p. 73-97.

Physics

Celestial Mechanics, Differential Equations, Lunar Orbits, Operational Calculus, Difference Equations, Laplace Transformation, Volterra Equations

Scientific paper

Hill's differential equation of lunar theory is solved by a method which avoids the cumbersome infinite determinants of the classical procedure. The Laplace transform is used to obtain a difference equation with an infinite number of terms and variable coefficients. When the first member is divided by a suitable factor the difference equation becomes the image of a Volterra equation which is equivalent to the initial Hill equation. The solution of this Volterra equation is unique and turns out to be the general solution of the Hill equation

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