 | | Journal of Applied
Mathematics and Mechanics
Russian Academy of Sciences | | Founded
in January 1936
(Translated from 1958)
Issued 6 times a year
ISSN 0021-8928
(print version) |
Archive of Issues
| Total articles in the database: | | 10522 |
| In Russian (ΟΜΜ): | | 9723
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| In English (J. Appl. Math. Mech.): | | 799 |
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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, blinovap@gmail.com) |
| 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 |
04 May 2009 |
| Link to Fulltext |
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