On the non-existence of the additional integral in the problem of the motion of a heavy rigid ellipsoid along a smooth planeстатья
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Аннотация:Two cases are known, in which the system of equations of motion of a heavy rigid body along a smooth plane is Liouville integrable (see e.g. /1/); in one the body is a sphere whose centre of mass coincides with its geometrical centre and the moments of inertia are arbitrary, and in the other the body is a solid of revolution. In the present paper the necessary conditions for an additional first integral to exist, analytic with respect to the plane variables, is obtained for ellipsoidal bodies resembling a sphere whose principal moments of inertia are different and whose centre of mass coincides with the geometrical centre.