Differential Galois Approach to the Non-integrability of the Heavy Top Problem

Simple item page
dc.creatorMaciejewski, Andrzej J.
dc.creatorPrzybylska, Maria
dc.date2004-04-20
dc.date.accessioned2026-07-07T07:43:32Z
dc.date.available2026-07-07T07:43:32Z
dc.descriptionWe study integrability of the Euler-Poisson equations describing the motion of a rigid body with one fixed point in a constant gravity field. Using the Morales-Ramis theory and tools of differential algebra we prove that a symmetric heavy top is integrable only in the classical cases of Euler, Lagrange, and Kovalevskaya and is partially integrable only in the Goryachev-Chaplygin case. Our proof is alternative to that given by Ziglin ({\em Funktsional. Anal. i Prilozhen.}, 17(1):8--23, 1983; {\em Funktsional. Anal. i Prilozhen.}, 31(1):3--11, 95, 1997).
dc.description31 pages, 1 figure
dc.identifierhttps://arxiv.org/abs/math/0404367
dc.identifierhttp://arxiv.org/abs/math/0404367
dc.identifierAnn. Fac. Sci. Toulouse Math. (6), 2005, vol.14, no.1, pp.123--160
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/122865
dc.subjectDynamical Systems
dc.subjectMathematical Physics
dc.subjectExactly Solvable and Integrable Systems
dc.subject70Exx
dc.titleDifferential Galois Approach to the Non-integrability of the Heavy Top Problem
dc.typetext

Files

Collections

arXiv