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

✍ Scribed by M.Yu. Ivochkin

• Publisher: Elsevier Science
• Year: 2009
• Tongue: English
• Weight: 201 KB
• Volume: 73
• Category: Article
• ISSN: 0021-8928
• DOI: 10.1016/j.jappmathmech.2009.11.015

✦ Synopsis

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).