{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:26:25Z","timestamp":1760059585949,"version":"build-2065373602"},"reference-count":14,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2025,6,21]],"date-time":"2025-06-21T00:00:00Z","timestamp":1750464000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In the classical problem of the motion of a rigid body around a fixed point, which is described by the Euler\u2013Poisson equations, we propose a new method for computing cases of integrability: first, we provide algorithms for computing values of parameters ensuring potential integrability, and then we select cases of global integrability. By this method we have obtained all the known cases of global integrability and six new cases of potential integrability for which the absence of their global integrability is proven.<\/jats:p>","DOI":"10.3390\/axioms14070484","type":"journal-article","created":{"date-parts":[[2025,6,23]],"date-time":"2025-06-23T07:42:34Z","timestamp":1750664554000},"page":"484","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Searching for New Integrals in the Euler\u2013Poisson Equations"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7465-1258","authenticated-orcid":false,"given":"Alexander D.","family":"Bruno","sequence":"first","affiliation":[{"name":"Keldysh Institute of Applied Mathematics of RAS, sq. Miusskaya 4, Moscow 125047, Russia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8871-4697","authenticated-orcid":false,"given":"Alexander B.","family":"Batkhin","sequence":"additional","affiliation":[{"name":"Keldysh Institute of Applied Mathematics of RAS, sq. Miusskaya 4, Moscow 125047, Russia"},{"name":"The Stephen B. Klein Faculty of Aerospace Engineering, Technion\u2013Israel Institute of Technology, Technion City, Haifa 3200003, Israel"}]}],"member":"1968","published-online":{"date-parts":[[2025,6,21]]},"reference":[{"key":"ref_1","unstructured":"Euler, L. (1758\u20131765). Recherches sur la Connoissance Mecanique des Corps, Histoire de l\u2019Academie Royale des Sciences. chapter Recherches sur la connoissance mecanique des corps."},{"key":"ref_2","unstructured":"Lagrange, J. (1811\u20131815). Mecanique Analytique, Mme Ve. 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(In Russian)."},{"key":"ref_7","unstructured":"Golubev, V.V. (1960). Lectures on Integration of the Equations of Motion of a Rigid Body About a Fixed Point, State Publishing House of Technical and Theoretical Literature. (In Russian)."},{"key":"ref_8","unstructured":"Bruno, A.D., and Batkhin, A.B. (2024, January 15\u201320). Chapter New cases of integrability of the Euler-Poisson system. Proceedings of the International Conference Polynomial Computer Algebra \u20192024, St. Petersburg, Russia."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"168","DOI":"10.1016\/j.jappmathmech.2007.06.002","article-title":"Analysis of the Euler\u2013Poisson equations by methods of power geometry and normal form","volume":"71","author":"Bruno","year":"2007","journal-title":"J. Appl. Math. Mech."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1007\/s11786-023-00567-6","article-title":"Integrable Cases of the Polynomial Li\u00e9nard-type Equation with Resonance in the Linear Part","volume":"17","author":"Edneral","year":"2023","journal-title":"Math. Comput. Sci."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"410","DOI":"10.1134\/S1560354716040031","article-title":"Holomorphic normal form of nonlinear perturbations of nilpotent vector fields","volume":"21","author":"Stolovitch","year":"2016","journal-title":"Regul. Chaotic Dyn."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1002\/cpa.3160110208","article-title":"On the generalization of a theorem of A. liapounoff","volume":"11","author":"Moser","year":"1958","journal-title":"Commun. Pure Appl. Math."},{"key":"ref_13","unstructured":"Nayfeh, A.H. (2011). The Method of Normal Forms, Wiley-VCH Verlag GmbH & Co. KGaA."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Yehia, H.M. (2022). Rigid Body Dynamics. A Lagrangian Approach, Birkh\u00e4user. Advances in Mechanics and Mathematics.","DOI":"10.1007\/978-3-030-96336-1"}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/7\/484\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T17:56:16Z","timestamp":1760032576000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/7\/484"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,6,21]]},"references-count":14,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2025,7]]}},"alternative-id":["axioms14070484"],"URL":"https:\/\/doi.org\/10.3390\/axioms14070484","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2025,6,21]]}}}