Celestial Mechanics and Dynamical Astronomy

, Volume 129, Issue 4, pp 433–448 | Cite as

3-Dimensional Necklace Flower Constellations

  • David Arnas
  • Daniel Casanova
  • Eva Tresaco
  • Daniele Mortari
Original Article

Abstract

A new approach in satellite constellation design is presented in this paper, taking as a base the 3D Lattice Flower Constellation Theory and introducing the necklace problem in its formulation. This creates a further generalization of the Flower Constellation Theory, increasing the possibilities of constellation distribution while maintaining the characteristic symmetries of the original theory in the design.

Keywords

Satellite constellations Orbit design Number theory 

Notes

Acknowledgements

The work of David Arnas, Daniel Casanova, and Eva Tresaco was supported by the Spanish Ministry of Economy and Competitiveness (Project No. ESP2013–44217–R) and the Research Group E48: GME.

References

  1. Arnas, D., Casanova, D., Tresaco, E.: Corrections on repeating ground-track orbits and their applications in satellite constellation design. Adv. Astronaut. Sci. 158, 2823–2840 (2016a) ISBN:978-0-87703-634-0Google Scholar
  2. Arnas, D., Casanova, D., Tresaco, E.: Relative and absolute station-keeping for two-dimensional-lattice flower constellations. J. Guid. Control Dyn. 39(11), 2596–2602 (2016b). doi: 10.2514/1.G000358 ADSCrossRefGoogle Scholar
  3. Arnas, D., Casanova, D., Tresaco, E.: 2D necklace flower constellations. Submitted to Acta Astronaut (2017a)Google Scholar
  4. Arnas, D., Casanova, D., Tresaco, E., Mortari, D.: 3D lattice flower constellations using necklaces. AAS/AIAA 17-234 Space Flight Mechanics Meeting, San Antonio, TX (2017b)Google Scholar
  5. Arnas, D., Casanova, D., Tresaco, E.: Time distributions in satellite constellation design. Celest. Mech. Dyn. Astron. 128(2), 197–219 (2017c). doi: 10.1007/s10569-016-9747-3 ADSCrossRefMathSciNetGoogle Scholar
  6. Arnas, D., Fialho, M.A.A., Mortari, D.: Fast and robust kernel generators for star trackers. Acta Astronaut. 134, 291–302 (2017d). doi: 10.1016/j.actaastro.2017.02.016
  7. Avendaño, M.E., Davis, J.J., Mortari, D.: The 2-D lattice theory of flower constellations. Celest. Mech. Dyn. Astron. 116(4), 325–337 (2013). doi: 10.1007/s10569-013-9493-8 ADSCrossRefMathSciNetGoogle Scholar
  8. Casanova, D., Avendaño, M.E., Mortari, D.: Necklace theory on flower constellations. Adv. Astronaut. Sci. 140, 1791–1804 (2011)Google Scholar
  9. Casanova, D., Avendaño, M.E., Mortari, D.: Design of flower constellations using necklaces. J. IEEE Trans. Aerosp. Electron. Syst. 50(2), 1347–1358 (2014a). doi: 10.1109/TAES.2014.120269
  10. Casanova, D., Avendaño, M.E., Tresaco, E.: Lattice-preserving flower constellations under J2 perturbations. Celest. Mech. Dyn. Astron. 121(1), 83–100 (2014b). doi: 10.1007/s10569-014-9583-2 ADSCrossRefGoogle Scholar
  11. Cattell, K., Ruskey, F., Sawada, J., Serra, M., Miers, R.: Fast algorithms to generate necklaces, unlabeled necklaces, and irreducible polynomials over GF(2). J. Algorithm 37(2), 267–282 (2000). doi: 10.1006/jagm.2000.1108 CrossRefMATHMathSciNetGoogle Scholar
  12. Davis, J.J., Avendaño, M.E., Mortari, D.: The 3-D lattice theory of flower constellations. Celest. Mech. Dyn. Astron. 116(4), 339–356 (2013). doi: 10.1007/s10569-013-9494-7 ADSCrossRefMathSciNetGoogle Scholar
  13. Draim, J.E.: A common-period four-satellite continuous global coverage constellation. J. Guid. Control Dyn. 10(5), 492–499 (1987) ISSN:0731-5090Google Scholar
  14. Mortari, D., Wilkins, M.P.: Flower constellation set theory part I: compatibility and phasing. J. IEEE Trans. Aerosp. Electron. Syst. 44(3), 953–963 (2008). doi: 10.1109/TAES.2008.4655355 ADSCrossRefGoogle Scholar
  15. Mortari, D., Wilkins, M.P., Bruccoleri, C.: The flower constellations. J. Astronaut. Sci. Am. Astronaut. Soc. 52(1–2), 107–127 (2004)MathSciNetGoogle Scholar
  16. Sawada, J.: A fast algorithm to generate necklaces with fixed content. Theor. Comput. Sci. 301, 277–289 (2003). doi: 10.1016/S0304-3975(03)00049-5 CrossRefMATHMathSciNetGoogle Scholar
  17. Walker, J.G.: Satellite constellations. J. Br. Interplanet. Soc. 37, 559–572 (1984)ADSGoogle Scholar
  18. Wilkins, M.P., Mortari, D.: Flower constellation set theory part II: secondary paths and equivalency. J. IEEE Trans. Aerosp. Electron. Syst. 44(3), 964–976 (2008). doi: 10.1109/TAES.2008.4655356 ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  1. 1.Centro Universitario de la Defensa - ZaragozaIUMA - Universidad de ZaragozaZaragozaSpain
  2. 2.Centro Universitario de la Defensa - Zaragoza GME - IUMA - Universidad de ZaragozaZaragozaSpain
  3. 3.Aerospace EngineeringTexas A&M UniversityCollege StationUSA

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