A complex exponential solution to the unified two-body problem Academic Article

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. Springer Science+Business Media B.V. 2009.

authors

• Junkins, John

published proceedings

• CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY

author list (cited authors)

• Henderson, T. A., Junkins, J. L., & Radice, G.

citation count

• 1

complete list of authors

• Henderson, Troy A||Junkins, John L||Radice, Gianmarco

publication date

• August 2009

publisher

• Springer Nature  Publisher

keywords

• Complex Exponential
• Elliptic And Hyperbolic Solutions
• Sundman Transformation
• Unified Two-body Problem

Digital Object Identifier (DOI)

• 10.1007/s10569-009-9218-1

start page

• 355

end page

• 368

volume

• 104

issue

• 4

URL

• http%3A%2F%2Fdx.doi.org%2F10.1007%2Fs10569-009-9218-1