The 2-D lattice theory of Flower Constellations
Abstract
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 2× 2 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 J_2 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.
- Publication:
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Celestial Mechanics and Dynamical Astronomy
- Pub Date:
- August 2013
- DOI:
- 10.1007/s10569-013-9493-8
- Bibcode:
- 2013CeMDA.116..325A
- Keywords:
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- Satellite constellations design;
- Lattice flower constellation;
- Hermite normal forms