Searching for New Integrals in the Euler–Poisson Equations
In the classical problem of the motion of a rigid body around a fixed point, which is described by the Euler–Poisson 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...
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| Language: | English |
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MDPI AG
2025-06-01
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| Online Access: | https://www.mdpi.com/2075-1680/14/7/484 |
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| author | Alexander D. Bruno Alexander B. Batkhin |
| author_facet | Alexander D. Bruno Alexander B. Batkhin |
| author_sort | Alexander D. Bruno |
| collection | DOAJ |
| description | In the classical problem of the motion of a rigid body around a fixed point, which is described by the Euler–Poisson 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. |
| format | Article |
| id | doaj-art-32daa29fb85643c795dc45a262697c1e |
| institution | Kabale University |
| issn | 2075-1680 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj-art-32daa29fb85643c795dc45a262697c1e2025-08-20T03:35:27ZengMDPI AGAxioms2075-16802025-06-0114748410.3390/axioms14070484Searching for New Integrals in the Euler–Poisson EquationsAlexander D. Bruno0Alexander B. Batkhin1Keldysh Institute of Applied Mathematics of RAS, sq. Miusskaya 4, Moscow 125047, RussiaKeldysh Institute of Applied Mathematics of RAS, sq. Miusskaya 4, Moscow 125047, RussiaIn the classical problem of the motion of a rigid body around a fixed point, which is described by the Euler–Poisson 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.https://www.mdpi.com/2075-1680/14/7/484rigid topEuler–Poisson equationsintegrabilitynormal form |
| spellingShingle | Alexander D. Bruno Alexander B. Batkhin Searching for New Integrals in the Euler–Poisson Equations Axioms rigid top Euler–Poisson equations integrability normal form |
| title | Searching for New Integrals in the Euler–Poisson Equations |
| title_full | Searching for New Integrals in the Euler–Poisson Equations |
| title_fullStr | Searching for New Integrals in the Euler–Poisson Equations |
| title_full_unstemmed | Searching for New Integrals in the Euler–Poisson Equations |
| title_short | Searching for New Integrals in the Euler–Poisson Equations |
| title_sort | searching for new integrals in the euler poisson equations |
| topic | rigid top Euler–Poisson equations integrability normal form |
| url | https://www.mdpi.com/2075-1680/14/7/484 |
| work_keys_str_mv | AT alexanderdbruno searchingfornewintegralsintheeulerpoissonequations AT alexanderbbatkhin searchingfornewintegralsintheeulerpoissonequations |