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...

Full description

Saved in:
Bibliographic Details
Main Authors: Alexander D. Bruno, Alexander B. Batkhin
Format: Article
Language:English
Published: MDPI AG 2025-06-01
Series:Axioms
Subjects:
Online Access:https://www.mdpi.com/2075-1680/14/7/484
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1849409627793391616
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