The necessary conditions for the existence of an additional integral in the problem of the motion of a heavy ellipsoid on a smooth horizontal plane

The equations of motion of an ellipsoid on a smooth horizontal plane are similar to the equations of motion of a heavy rigid body with a fixed point. In general, one integral is also lacking in order to integrate them. For a triaxial ellipsoid, the centre of mass of which coincides with the geometri...

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Veröffentlicht in:Journal of applied mathematics and mechanics 2009, Vol.73 (5), p.616-620
1. Verfasser: Ivochkin, M.Yu
Format: Artikel
Sprache:eng
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Zusammenfassung:The equations of motion of an ellipsoid on a smooth horizontal plane are similar to the equations of motion of a heavy rigid body with a fixed point. In general, one integral is also lacking in order to integrate them. For a triaxial ellipsoid, the centre of mass of which coincides with the geometrical centre, it is proved that an additional integral is lacking (in the generic case).
ISSN:0021-8928
0021-8928
DOI:10.1016/j.jappmathmech.2009.11.015