Equations of Motion Using the Dynamical Evolution of the RungeLenz Vector
Abstract
Based on the dynamical evolution of the RungeLenz vector, a set of firstorder differential equations of motion for the calculation of orbits for arbitrary forces is given. The corresponding orbit equation is explicitly expressed via the timedependent RungeLenz vector ∊ as a local conic section relative to ∊, with the local eccentricity given by ∊. 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 threebody problem.
 Publication:

The Astrophysical Journal
 Pub Date:
 November 1988
 DOI:
 10.1086/166856
 Bibcode:
 1988ApJ...334..517B
 Keywords:

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