{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T00:46:41Z","timestamp":1760230001984,"version":"build-2065373602"},"reference-count":15,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2022,7,5]],"date-time":"2022-07-05T00:00:00Z","timestamp":1656979200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"RUDN University"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The dynamics of a particle in 3:1 tesseral resonance with the dwarf planet Haumea is analysed. This resonance, three rotations of the primary per orbital period of the particle, is located inside the region where Haumea\u2019s ring was observed. Thus, determining the effect of this resonance on a particle\u2019s orbit reveals its relationship to the orbits that follow the particles of the ring. To analyse the effect, we propose four models of anisotropy; two of them are a reduced representation of the distribution of the mass of Haumea that we use to determine the centre of the resonance by means of the Hamiltonian formulation. After this, we analyse the effects of the four models on the resonance orbit by using the Lagrange planetary equations technique. The results show that the resonance centre has a high eccentricity value, meaning that a particle in 3:1 resonance with Haumea does not remain confined to the region that we consider to be the ring region.<\/jats:p>","DOI":"10.3390\/sym14071378","type":"journal-article","created":{"date-parts":[[2022,7,6]],"date-time":"2022-07-06T21:15:52Z","timestamp":1657142152000},"page":"1378","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Dynamics of a Particle in 3:1 Tesseral Resonance with the Dwarf Planet Haumea"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6041-756X","authenticated-orcid":false,"given":"Dairo Antonio","family":"Cuellar Mateus","sequence":"first","affiliation":[{"name":"Space Mechanics and Control Division (CMC), National Institute for Space Research, Av dos Astronautas, 1758, S\u00e3o Jos\u00e9 dos Campos 12227-010, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ant\u00f4nio F. B. A.","family":"Prado","sequence":"additional","affiliation":[{"name":"Academy of Engineering, Peoples\u2019 Friendship University of Russia (RUDN University), 6 Miklukho Maklaya, 117198 Moscow, Russia"},{"name":"Postgraduate Division, National Institute for Space Research (INPE), S\u00e3o Jos\u00e9 dos Campos 12227-010, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3878-3931","authenticated-orcid":false,"given":"Diogo Merguizo","family":"Sanchez","sequence":"additional","affiliation":[{"name":"Space Mechanics and Control Division (CMC), National Institute for Space Research, Av dos Astronautas, 1758, S\u00e3o Jos\u00e9 dos Campos 12227-010, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rodolpho Vilhena","family":"de Moraes","sequence":"additional","affiliation":[{"name":"Space Mechanics and Control Division (CMC), National Institute for Space Research, Av dos Astronautas, 1758, S\u00e3o Jos\u00e9 dos Campos 12227-010, Brazil"},{"name":"UNIFESP\u2014Instituto de Ci\u00eancia e Tecnologia, Universidade Federal de S\u00e3o Paulo, S\u00e3o Jos\u00e9 dos Campos 12247-014, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,7,5]]},"reference":[{"key":"ref_1","unstructured":"Ortiz, J.L., Santos-Sanz, P., Sicardy, B., Benedetti-Rossi, G., B\u00e9rard, D., Morales, N., Duffard, R., Braga-Ribas, F., Hopp, U., and Ries, C. (2017). The Size, Shape, Density and Ring of the Dwarf Planet Haumea from Stellar Occultation, Macmillam Publishers Limited (Springer Nature)."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"4766","DOI":"10.1088\/0004-6256\/137\/6\/4766","article-title":"Orbits and masses of the satellites of the dwarf planet Haumea (2003 EL61)","volume":"137","author":"Ragozzine","year":"2009","journal-title":"Astron. J."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"4560","DOI":"10.1093\/mnras\/sty1849","article-title":"Dynamics of Haumea\u2019s dust ring","volume":"479","author":"Kovacs","year":"2018","journal-title":"Mon. Not. R. Astron. Soc."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"3765","DOI":"10.1093\/mnras\/stz246","article-title":"On the location of the ring around the dwarf planet Haumea","volume":"484","author":"Winter","year":"2019","journal-title":"Mon. Not. R. Astron. Soc."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"2085","DOI":"10.1093\/mnras\/staa1696","article-title":"Perturbation Maps and the ring of Haumea","volume":"496","author":"Sanchez","year":"2020","journal-title":"Mon. Not. R. Astron. Soc."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"21","DOI":"10.3847\/1538-4357\/ab93bb","article-title":"N-body Simulations of the Ring Formation Process around the Dwarf Planet Haumea","volume":"897","author":"Sumida","year":"2020","journal-title":"Astrophys. J."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"A67","DOI":"10.1051\/0004-6361\/202038812","article-title":"Ring dynamics around an oblate body with an inclined satellite: The case of Haumea","volume":"643","author":"Marzari","year":"2020","journal-title":"Astron. Astrophys."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Garfinkel, B. (1970). On the ideal resonance problem. Periodic Orbits, Stability and Resonances, Springer.","DOI":"10.1007\/978-94-010-3323-7_40"},{"key":"ref_9","unstructured":"Fernandes, S., and Zanardi, M. (2018). Fundamentos de Astron\u00e1utica e Suas Aplica\u00e7oes, Editora UFABC."},{"key":"ref_10","unstructured":"Kaula, W.M. (1966). Theory of Satellite Geodesy\u2019, Blaisdell Publ. Co."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1007\/BF00691901","article-title":"Gravitational potential harmonics from the shape of an homogeneous body","volume":"60","author":"Balmino","year":"1994","journal-title":"Celest. Mech. Dyn. Astron."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"105185","DOI":"10.1016\/j.cnsns.2020.105185","article-title":"Resonances in the Earth\u2019s space environment","volume":"84","author":"Celletti","year":"2020","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"ref_13","unstructured":"Morbidelli, A. (2002). Modern Celestial Mechanics: Aspects of Solar System Dynamics, Taylor & Francis."},{"key":"ref_14","unstructured":"Lanczos, C. (1952). The Variational Principles of Mechanics, Oxford University Press."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"de Iaco Veris, A. (2018). Practical Astrodynamics, Springer.","DOI":"10.1007\/978-3-319-62220-0"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/7\/1378\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T23:42:47Z","timestamp":1760139767000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/7\/1378"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,7,5]]},"references-count":15,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2022,7]]}},"alternative-id":["sym14071378"],"URL":"https:\/\/doi.org\/10.3390\/sym14071378","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2022,7,5]]}}}