A state transition matrix using complex exponentials for the two-body problem

Henderson, T., Radice, G. and Junkins, J. (2008) A state transition matrix using complex exponentials for the two-body problem. Advances in the Astronautical Sciences, 130(1-2), pp. 1853-1861.

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Previously, a complex exponential solution was derived which unified the elliptic and hyperbolic trajectories into a single set of equations1 and provided an exact analytical solution to the unperturbed two-body problem. The formulation eliminates singularities associated with the elliptical and hyperbolic trajectories that arise from these orbit trajectories. Using this complex exponential solution formulation, the state transition matrix has been analytically derived and is presented. We present the analytical state transition matrix formulation and highlight the benefits of this approach compared with the classical developments.

Item Type:Articles
Additional Information:SPACEFLIGHT MECHANICS 2008, VOL 130, PTS 1 AND 2 978-0-87703-544-2
Keywords:Lyapunov method, potential functions, CMG actuators, spacecraft attitude control.
Glasgow Author(s) Enlighten ID:Radice, Dr Gianmarco
Authors: Henderson, T., Radice, G., and Junkins, J.
Subjects:Q Science > QB Astronomy
Q Science > QA Mathematics
College/School:College of Science and Engineering > School of Engineering > Autonomous Systems and Connectivity
Research Group:Space Advanced Research Team
Journal Name:Advances in the Astronautical Sciences

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