A complex exponential solution to the unified two-body problem

Henderson, T.A., Junkins, J.L. and Radice, G. (2009) A complex exponential solution to the unified two-body problem. Celestial Mechanics and Dynamical Astronomy, 104(4), pp. 355-368. (doi: 10.1007/s10569-009-9218-1)

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Publisher's URL: http://dx.doi.org/10.1007/s10569-009-9218-1


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.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Radice, Dr Gianmarco
Authors: Henderson, T.A., Junkins, J.L., and Radice, G.
College/School:College of Science and Engineering > School of Engineering > Autonomous Systems and Connectivity
Journal Name:Celestial Mechanics and Dynamical Astronomy

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