A complex exponential solution to the unified two-body problem |
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| Authors: | Troy A Henderson John L Junkins Gianmarco Radice |
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| Institution: | (1) Department of Aerospace Engineering, Texas A&M University, 3141 TAMU, College Station, TX 77843-3141, USA;(2) Depatment of Aerospace Engineering, University of Glasgow, James Watt South Building, University Avenue, Glasgow, G12 8QQ, UK |
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| 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.
Previously presented as AAS 07-136 at the 17th AAS/AIAA Spaceflight Mechanics Meeting Sedona, Arizona, AAS 08-206 and AAS
08-230 at the 18th AAS/AIAA Spaceflight Mechanics Meeting Galveston, Texas. |
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| Keywords: | Sundman transformation Complex exponential Unified two-body problem Elliptic and hyperbolic solutions |
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