 | | 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: | | 10512 |
| In Russian (ΟΜΜ): | | 9713
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| In English (J. Appl. Math. Mech.): | | 799 |
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| << Previous article | Volume 81, Issue 4 / 2017 | Next article >> |
| A.P. Markeev, "On stability in a case of oscillations of a pendulum with a mobile point mass," J. Appl. Math. Mech. 81 (4), 262-269 (2017) |
| Year |
2017 |
Volume |
81 |
Issue |
4 |
Pages |
262-269 |
| DOI |
10.1016/j.jappmathmech.2017.12.003 |
| Title |
On stability in a case of oscillations of a pendulum with a mobile point mass |
| Author(s) |
A.P. Markeev (Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow, Russia, markeev@ipmnet.ru) |
| Abstract |
Motion in a uniform gravitational field of a modified pendulum in the form of a thin, uniform rod, one end of which is attached by a hinge, is investigated. A point mass (for example, a washer mounted on the rod) can move without friction along the rod. From time to time, the point mass collides with the other end of the rod (if, for example, at this end of the rod a rigid plate of negligibly small mass is attached perpendicular to it). The collisions are assumed to be perfectly elastic. There exists such a motion of the pendulum in which the rod is at rest (it hangs) along the vertical passing through its suspension point, but the point mass moves along the rod, periodically bouncing up from its lower end to some height not exceeding the rod length. The nonlinear problem of the orbital stability of this periodic motion of the pendulum is investigated. In the space of two dimensionless parameters of the problem, stability and instability regions are found. |
| Received |
26 January 2017 |
| Link to Fulltext |
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| << Previous article | Volume 81, Issue 4 / 2017 | Next article >> |
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