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)

Abstract

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
• Status: Published
• Refereed: Yes
• 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
• ISSN: 0923-2958