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Application of the Kovacic algorithm for the investigation of motion of a heavy rigid body with a fixed point in the Hess case.
- Source :
- ZAMM -- Journal of Applied Mathematics & Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik; Nov2022, Vol. 102 Issue 11, p1-21, 21p
- Publication Year :
- 2022
-
Abstract
- In 1890, Hess found new special case of integrability of Euler–Poisson equations of motion of a heavy rigid body with a fixed point. In 1892, Nekrasov proved that the solution of the problem of motion of a heavy rigid body with a fixed point under Hess conditions reduces to integrating the second‐order linear differential equation. In this paper, the corresponding linear differential equation is derived and its coefficients are presented in the rational form. Using the Kovacic algorithm, we proved that the Liouvillian solutions of the corresponding second‐order linear differential equation exist only in the case, when the moving rigid body is the Lagrange top, or in the case, when the constant of the area integral is zero. In 1890, Hess found new special case of integrability of Euler–Poisson equations of motion of a heavy rigid body with a fixed point. In 1892, Nekrasov proved that the solution of the problem of motion of a heavy rigid body with a fixed point under Hess conditions reduces to integrating the second‐order linear differential equation. In this paper, the corresponding linear differential equation is derived and its coefficients are presented in the rational form.... [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00442267
- Volume :
- 102
- Issue :
- 11
- Database :
- Complementary Index
- Journal :
- ZAMM -- Journal of Applied Mathematics & Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik
- Publication Type :
- Academic Journal
- Accession number :
- 160097816
- Full Text :
- https://doi.org/10.1002/zamm.202100036