Journal
CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY
Volume 116, Issue 4, Pages 325-337Publisher
SPRINGER
DOI: 10.1007/s10569-013-9493-8
Keywords
Satellite constellations design; Lattice flower constellation; Hermite normal forms
Funding
- NSF [OISE-I004064]
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The 2-D lattice theory of Flower Constellations, generalizing Harmonic Flower Constellations (the symmetric subset of Flower Constellations) as well as the Walker/ Mozhaev constellations, is presented here. This theory is a new general framework to design symmetric constellations using a lattice matrix of integers or by its minimal representation, the Hermite normal form. From a geometrical point of view, the phasing of satellites is represented by a regular pattern (lattice) on a two-Dimensional torus. The 2-D lattice theory of Flower Constellations does not require any compatibility condition and uses a minimum set of integer parameters whose meaning are explored throughout the paper. This general minimum-parametrization framework allows us to obtain all symmetric distribution of satellites. Due to the effect this design framework is meant for circular orbits and for elliptical orbits at critical inclination, or to design elliptical constellations for the unperturbed Keplerian case.
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