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Russian Academy of Sciences
in January 1936
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IssuesArchive of Issues2011-2pp.171-175

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A.P. Blinov, "The motion of a point mass on the surface of a smooth funnel," J. Appl. Math. Mech. 75 (2), 171-175 (2011)
Year 2011 Volume 75 Issue 2 Pages 171-175
Title The motion of a point mass on the surface of a smooth funnel
Author(s) A.P. Blinov (Moscow, Russia,
Abstract The motion of a point mass on a smooth concave surface (a funnel) under the action of a gravitational force is considered. The equations of motion are reduced to a form to which Lyapunov's theorem on the representation of the solution in the form of power series in the initial conditions, which converge absolutely in a finite region of phase space is applied. In the non-local formulation of the problem, a procedure is described for estimating the libration periods, based on an analysis of geometric forms. A bilateral estimate of the region of possible motion of the point is given for rotational-type motions, when the funnel is a surface of revolution.
Received 4 May 2009
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