Variational and symplectic integrators for satellite relative orbit propagation including drag

  • Leonel Palacios
  • Pini Gurfil
Original Article


Orbit propagation algorithms for satellite relative motion relying on Runge–Kutta integrators are non-symplectic—a situation that leads to incorrect global behavior and degraded accuracy. Thus, attempts have been made to apply symplectic methods to integrate satellite relative motion. However, so far all these symplectic propagation schemes have not taken into account the effect of atmospheric drag. In this paper, drag-generalized symplectic and variational algorithms for satellite relative orbit propagation are developed in different reference frames, and numerical simulations with and without the effect of atmospheric drag are presented. It is also shown that high-order versions of the newly-developed variational and symplectic propagators are more accurate and are significantly faster than Runge–Kutta-based integrators, even in the presence of atmospheric drag.


Symplectic integration Variational integration Geometric numerical integration Satellite relative motion Hamiltonian dynamics 


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© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Mechanical and Aerospace EngineeringPrinceton UniversityPrincetonUSA
  2. 2.Faculty of Aerospace EngineeringTechnion – Israel Institute of TechnologyHaifaIsrael

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