Fourier expansions of rational fractions of elliptic integrals and Jacobian elliptic functions
Abstract
Recent work in earth satellite orbit theory, earthmoon trajectory theory and close binary systems has revived the interest in the twofixedcenters problem, the twocenter orbit serving as an intermediate orbit. Elliptic functions arise naturally in such problems; treatment of perturbations involves Fourier expansions of certain combinations of elliptic functions and elliptic integrals. Availability of these expansions eliminates or greatly reduces the number of Fourier series multiplications that otherwise appear in orbit theory. Where elliptical integrals of the third kind appear, it is the circular case that is of interest. In the present paper, the pertinent expansions are derived for this case.
 Publication:

SIAM Journal of Mathematical Analysis
 Pub Date:
 May 1980
 Bibcode:
 1980SJMA...11..506L
 Keywords:

 EarthMoon Trajectories;
 Elliptic Functions;
 Fourier Series;
 Integral Transformations;
 Orbital Mechanics;
 Satellite Orbits;
 Binary Stars;
 Fractions;
 Jacobi Integral;
 Orbit Calculation;
 Orbit Perturbation;
 Rational Functions;
 Astronomy