Equations of motion using the dynamical evolution of the Runge-Lenz vector

Details Equations of motion using the dynamical evolution of the Runge-Lenz vector Equations of motion using the dynamical evolution of the Runge-Lenz vector

Nov 1988

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1988apj...334..517b&link_type=abstract

Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 334, Nov. 1, 1988, p. 517-526.

Statistics

Computation

3

Asteroids, Celestial Mechanics, Dynamic Characteristics, Equations Of Motion, Planetary Orbits, Vector Analysis, Computational Astrophysics, Gravitational Fields, Three Body Problem, Time Dependence

Scientific paper

Based on the dynamical evolution of the Runge-Lenz vector, a set of first-order differential equations of motion for the calculation of orbits for arbitrary forces is given. The corresponding orbit equation is explicitly expressed via the time-dependent Runge-Lenz vector ɛ as a local conic section relative to ɛ, with the local eccentricity given by |ɛ|. While completely general, this approach is particularly well suited for those problems in celestial mechanics which can be formulated as pertubations of the Kepler case. As an example, the authors treat the motion of an asteroid in the gravitational force fields of the Sun and Jupiter within framework of the classical restricted three-body problem.

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