Abstract:
Two integrable problems are considered: the geodesic flow of an ellipsoid (the Jacobi problem) and the rotation of a solid about its center of mass (the Euler problem). It is proved that transforming the dynamical system of the Euler problem into the dynamical system of the Jacobi problem by a continuous change of coordinates is impossible.
Citation:
O. E. Orel, “The Euler problem in solid body dynamics and the Jacobi problem about geodesics on an ellipsoid are not topologically conjugate”, Mat. Zametki, 61:2 (1997), 252–258; Math. Notes, 61:2 (1997), 206–211
\Bibitem{Ore97}
\by O.~E.~Orel
\paper The Euler problem in solid body dynamics and the Jacobi problem about geodesics on an ellipsoid are not topologically conjugate
\jour Mat. Zametki
\yr 1997
\vol 61
\issue 2
\pages 252--258
\mathnet{http://mi.mathnet.ru/mzm1498}
\crossref{https://doi.org/10.4213/mzm1498}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1619935}
\zmath{https://zbmath.org/?q=an:0917.58012}
\transl
\jour Math. Notes
\yr 1997
\vol 61
\issue 2
\pages 206--211
\crossref{https://doi.org/10.1007/BF02355730}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1997XM39800023}
Linking options:
https://www.mathnet.ru/eng/mzm1498
https://doi.org/10.4213/mzm1498
https://www.mathnet.ru/eng/mzm/v61/i2/p252
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