000101511 001__ 101511 000101511 005__ 20240122154814.0 000101511 0247_ $$2doi$$a10.1016/j.asr.2020.04.045 000101511 0248_ $$2sideral$$a118257 000101511 037__ $$aART-2021-118257 000101511 041__ $$aeng 000101511 100__ $$0(orcid)0000-0002-8507-4679$$aArnas, D. 000101511 245__ $$an-Dimensional congruent lattices using necklaces 000101511 260__ $$c2021 000101511 5060_ $$aAccess copy available to the general public$$fUnrestricted 000101511 5203_ $$aThis work introduces the n-dimensional congruent lattices using necklaces, a general methodology to generate uniform distributions in multidimensional modular spaces. The formulation presented in this manuscript constitutes the mathematical foundation of the most used satellite constellation designs, including Walker Constellations, and Lattice and Necklace Flower Constellations. These constellation design models are based on Number Theory and allow to obtain distributions that have some interesting properties of uniformity and large number of symmetries. This work includes the complete formulation of the methodology, proofs for existence and uniqueness of the distribution definitions, and several theorems that focus on the counting possibilities of design for the most common cases of study. 000101511 536__ $$9info:eu-repo/grantAgreement/ES/DGA-FSE/E24-17R$$9info:eu-repo/grantAgreement/ES/MINECO-AEI-FEDER/ESP2017-87113-R 000101511 540__ $$9info:eu-repo/semantics/openAccess$$aAll rights reserved$$uhttp://www.europeana.eu/rights/rr-f/ 000101511 590__ $$a2.611$$b2021 000101511 592__ $$a0.613$$b2021 000101511 594__ $$a4.7$$b2021 000101511 591__ $$aENGINEERING, AEROSPACE$$b10 / 34 = 0.294$$c2021$$dQ2$$eT1 000101511 593__ $$aAerospace Engineering$$c2021$$dQ2 000101511 591__ $$aGEOSCIENCES, MULTIDISCIPLINARY$$b120 / 202 = 0.594$$c2021$$dQ3$$eT2 000101511 593__ $$aAstronomy and Astrophysics$$c2021$$dQ2 000101511 591__ $$aMETEOROLOGY & ATMOSPHERIC SCIENCES$$b66 / 94 = 0.702$$c2021$$dQ3$$eT3 000101511 593__ $$aSpace and Planetary Science$$c2021$$dQ2 000101511 591__ $$aASTRONOMY & ASTROPHYSICS$$b35 / 69 = 0.507$$c2021$$dQ3$$eT2 000101511 593__ $$aGeophysics$$c2021$$dQ2 000101511 593__ $$aAtmospheric Science$$c2021$$dQ2 000101511 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/acceptedVersion 000101511 700__ $$0(orcid)0000-0002-7620-4523$$aCasanova, D. 000101511 700__ $$0(orcid)0000-0003-4859-7224$$aTresaco, E. 000101511 773__ $$g67, 11 (2021), 3725-3743$$pAdv. space res.$$tAdvances in Space Research$$x0273-1177 000101511 85641 $$uhttps://www.sciencedirect.com/science/article/pii/S0273117720302970?dgcid=coauthor$$zTexto completo de la revista 000101511 8564_ $$s485351$$uhttps://zaguan.unizar.es/record/101511/files/texto_completo.pdf$$yPostprint 000101511 8564_ $$s2439119$$uhttps://zaguan.unizar.es/record/101511/files/texto_completo.jpg?subformat=icon$$xicon$$yPostprint 000101511 909CO $$ooai:zaguan.unizar.es:101511$$particulos$$pdriver 000101511 951__ $$a2024-01-22-15:33:44 000101511 980__ $$aARTICLE