Celestial Mechanics and Dynamical Astronomy

, Volume 122, Issue 4, pp 333–358 | Cite as

High order transfer maps for perturbed Keplerian motion

  • Alexander Wittig
  • Roberto ArmellinEmail author
Original Article


The paper presents a new semi-analytical technique for the propagation of near-Earth satellite motion. The approach uses differential algebra techniques to compute the high order expansion of the solution of the system’s ordinary differential equation for one orbital revolution, referred to as the transfer map. Once computed, a single high order transfer map (HOTM) can be reused to map an initial condition, or a set of initial conditions, forward in time for many revolutions. The only limiting factor is that the mapped objects must stay close to the reference orbit such that they remain within the region of validity of the HOTM. The performance of the method is assessed through a set of test cases in which both autonomous and non-autonomous perturbations are considered, including the case of continuously propelled trajectories.


Orbit propagation Perturbed Keplerian motion Differential algebra High-order transfer map method 



R. Armellin is grateful to Dr. Martín Lara for having provided a comprehensive overview of orbital propagation methods. A. Wittig gratefully acknowledges the support received by the EU Marie Curie ITN AstroNet-II (PITN-GA 2011-289240) through an experienced researcher fellowship. The authors thank Dr. Martin Berz for introducing them to Differential Algebra techniques and his fundamental work in establishing many of the concepts applied in this work in the field of beam and accelerator physics. Furthermore, we are in debt to Pierluigi Di Lizia. This work can be considered as another fruit of the many discussions we had while working together. Once he finishes drilling on 67P/Churyumov-Gerasimenko, we look forward to working with him again.


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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Department of Aerospace Science and TechnologyPolitecnico di MilanoMilanItaly
  2. 2.Aeronautics, Astronautics and Computational Engineering UnitUniversity of SouthamptonSouthamptonUK

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