3-Dimensional Necklace Flower Constellations

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.

[1]  David Arnas,et al.  Relative and Absolute Station-Keeping for Two-Dimensional–Lattice Flower Constellations , 2016 .

[2]  David Arnas,et al.  2D Necklace Flower Constellations , 2018 .

[3]  M. P. Wilkins,et al.  Flower constellation set theory part II: Secondary paths and equivalency , 2008, IEEE Transactions on Aerospace and Electronic Systems.

[4]  Daniele Mortari,et al.  The Flower Constellations , 2004 .

[5]  David Arnas,et al.  Time distributions in satellite constellation design , 2017 .

[6]  Daniele Mortari,et al.  The 2-D lattice theory of Flower Constellations , 2013 .

[7]  D. Mortari,et al.  Flower constellation set theory. Part I: Compatibility and phasing , 2008, IEEE Transactions on Aerospace and Electronic Systems.

[8]  John E. Draim,et al.  A common-period four-satellite continuous global coverage constellation , 1987 .

[9]  Daniele Mortari,et al.  Fast and robust kernel generators for star trackers , 2017 .

[10]  Joe Sawada,et al.  A fast algorithm to generate necklaces with fixed content , 2003, Theor. Comput. Sci..

[11]  Daniele Mortari,et al.  Design of flower constellations using necklaces , 2014, IEEE Transactions on Aerospace and Electronic Systems.

[12]  Frank Ruskey,et al.  Fast Algorithms to Generate Necklaces, Unlabeled Necklaces, and Irreducible Polynomials over GF(2) , 2000, J. Algorithms.

[13]  Daniele Mortari,et al.  The 3-D lattice theory of Flower Constellations , 2013 .

[14]  Daniel Casanova,et al.  Lattice-preserving Flower Constellations under $$J_2$$J2 perturbations , 2015 .