# Explicit evolution relations with orbital elements for eccentric, inclined, elliptic and hyperbolic restricted few-body problems

@article{Veras2014ExplicitER, title={Explicit evolution relations with orbital elements for eccentric, inclined, elliptic and hyperbolic restricted few-body problems}, author={Dimitri Veras}, journal={Celestial Mechanics and Dynamical Astronomy}, year={2014}, volume={118}, pages={315-353} }

Planetary, stellar and galactic physics often rely on the general restricted gravitational $$N$$N-body problem to model the motion of a small-mass object under the influence of much more massive objects. Here, I formulate the general restricted problem entirely and specifically in terms of the commonly used orbital elements of semimajor axis, eccentricity, inclination, longitude of ascending node, argument of pericentre, and true anomaly, without any assumptions about their magnitudes. I derive…

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