Celestial Mechanics and Dynamical Astronomy

, Volume 112, Issue 3, pp 253–282 | Cite as

Unified State Model theory and application in Astrodynamics

Open Access
Original Article


The Unified State Model is a method for expressing orbits using a set of seven elements. The elements consist of a quaternion and three parameters based on the velocity hodograph. A complete derivation of the original model is given in addition to two proposed modifications. Both modifications reduce the number of state elements from seven to six by replacing the quaternion with either modified Rodrigues parameters or the Exponential Map. Numerical simulations comparing the original Unified State Model, the Unified State Model with modified Rodrigues parameters, and the Unified State Model with Exponential Map, with the traditional Cartesian coordinates have been carried out. The Unified State Model and its derivatives outperform the Cartesian coordinates for all orbit cases in terms of accuracy and computational speed, except for highly eccentric perturbed orbits. The performance of the Unified State Model is exceptionally better for the case of orbits with continuous low-thrust propulsion with CPU simulation time being an order of magnitude lower than for the simulation using Cartesian coordinates. This makes the Unified State Model an excellent state propagator for mission optimizations.


Unified State Model Quaternion Modified Rodrigues parameters Orbit propagation Exponential map Hodograph 


Open Access

This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.


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Copyright information

© The Author(s) 2012

Authors and Affiliations

  1. 1.Faculty of Aerospace EngineeringDelft University of TechnologyDelftThe Netherlands

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