Structure preserving approximations of conservative forces for application to small-body dynamics

Andrew Colombi, Anil N. Hirani, Benjamin F. Villac

Research output: Contribution to journalArticle


Approximation-based methods, such as the cubetree algorithm, have proven to be significantly faster than traditional methods for complex force evaluations near small irregular bodies. Such methods also hold the promise of simplifying the inclusion of experimental data to update the force model. However, the cubetree algorithm does not preserve intrinsic properties of the gravitational force such as continuity, divergence freedom, or exactness. These properties may be needed for trajectory optimization, for the use of geometric (e.g., symplectic) integrators for longterm propagation, and for other trajectory design problems. This paper presents several adaptive schemes preserving global continuity, exactness, or divergence freedom, and discusses the difficulties involved in preserving all of these properties globally.

Original languageEnglish (US)
Pages (from-to)1847-1858
Number of pages12
JournalJournal of Guidance, Control, and Dynamics
Issue number6
StatePublished - Nov 1 2009


ASJC Scopus subject areas

  • Control and Systems Engineering
  • Aerospace Engineering
  • Space and Planetary Science
  • Electrical and Electronic Engineering
  • Applied Mathematics

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