Integrals of motion in the elliptic three-dimensional restricted three-body problem

Details Integrals of motion in the elliptic three-dimensional restricted three-body problem Integrals of motion in the elliptic three-dimensional restricted three-body problem

Apr 1982

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1982cemec..26..353s&link_type=abstract

Celestial Mechanics, vol. 26, Apr. 1982, p. 353-360.

Mathematics

Celestial Mechanics, Eccentric Orbits, Elliptical Orbits, Equations Of Motion, Three Body Problem, Three Dimensional Motion, Mass Ratios, Numerical Integration, Series (Mathematics)

Scientific paper

Three integrals of motion have been found in the three-dimensional elliptic restricted three-body problem for small eccentricity e-prime of the relative orbit of the primaries and small distance r and eccentricity e of the orbit of the third body around a primary. The integrals are given in the form of formal series in the mass-ratio, the eccentricities e-prime and e, and the coordinates and velocities. These integrals depend periodically on the time.

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