Astronomy and Astrophysics – Astronomy
Scientific paper
Aug 2009
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2009cemda.104..355h&link_type=abstract
Celestial Mechanics and Dynamical Astronomy, Volume 104, Issue 4, pp.355-368
Astronomy and Astrophysics
Astronomy
Sundman Transformation, Complex Exponential, Unified Two-Body Problem, Elliptic And Hyperbolic Solutions
Scientific paper
A complex exponential solution has been derived which unifies the elliptic and hyperbolic trajectories into a single set of equations and provides an exact, analytical solution to the unperturbed, Keplerian two-body problem. The formulation eliminates singularities associated with the elliptic and hyperbolic trajectories that arise from these orbits. Using this complex exponential solution formulation, a variation of parameters formulation for the perturbed two-body problem has been derived. In this paper, we present the analytical formulation of the complex exponential solution, numerical simulations, a comparison with classical solution methods, and highlight the benefits of this approach compared with the classical developments.
Henderson Troy A.
Junkins John L.
Radice Gianmarco
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