General planetary theory in elliptic functions View Full Text


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Article Info

DATE

1994-05

AUTHORS

V. A. Brumberg

ABSTRACT

It is shown that the first-order general planetary theory, i.e. the theory without secular terms, developed in (Brumberg and Chapront, 1973) may be re-constructed and presented by the series in powers of the eccentricity and inclination variables with the closed form coefficients expressed in terms of elliptic functions. The intermediate solution of the zero degree in eccentricities and inclinations has been given explicitly with the aid of elliptic functions and the Hansen type quadratures with trigonometric function kernels. In determining the first and higher degree terms in eccentricities and inclinations one meets the Hansen type quadratures with elliptic function kernels. The secular evolution is described by the autonomous polynomial differential system. More... »

PAGES

1-36

References to SciGraph publications

  • 1982-02. A third-order intermediate orbit for planetary theory in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 1978. Correspondances Entre Une Theorie Generale Planetarie en Variables Elliptiques et la Theorie Classique de le Verrier in DYNAMICS OF PLANETS AND SATELLITES AND THEORIES OF THEIR MOTION
  • 1987-09. First order planetary perturbations with elliptic functions in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 1973-11. Construction of a general planetary theory of the first order in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 1970. Application of Hill’s Lunar Method in General Planetary Theory in PERIODIC ORBITS, STABILITY AND RESONANCES
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    http://scigraph.springernature.com/pub.10.1007/bf00691969

    DOI

    http://dx.doi.org/10.1007/bf00691969

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