 | | 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: | | 10482 |
| In Russian (Ï̀̀): | | 9683
|
| In English (J. Appl. Math. Mech.): | | 799 |
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| << Previous article | Volume 80, Issue 4 / 2016 | Next article >> |
| K.V. Gugayev, P.A. Kruchinin, and A.M. Formalskii, "A model of maintaining balance by a person on the seesaw," J. Appl. Math. Mech. 80 (4), 316-323 (2016) |
| Year |
2016 |
Volume |
80 |
Issue |
4 |
Pages |
316-323 |
| DOI |
10.1016/j.jappmathmech.2016.09.006 |
| Title |
A model of maintaining balance by a person on the seesaw |
| Author(s) |
K.V. Gugayev (Lomonosov Moscow State University, Moscow, Russia)
P.A. Kruchinin (Lomonosov Moscow State University, Moscow, Russia, pkruch@mech.math.msu.su)
A.M. Formalskii (Lomonosov Moscow State University, Moscow, Russia, formal@imec.msu.ru) |
| Abstract |
A very simple model of the process of maintaining balance by a person standing on a seesaw is considered. The model consists of a planar single-link inverted pendulum, which is connected by means of a cylindrical hinge, i.e., an "ankle joint", to a support in the form of a segment of cylinder, whose axis is perpendicular to the pendulum. The support can oscillate by rolling on a horizontal surface, and the pendulum can oscillate in a plane that is perpendicular to the cylinder axis. The control is a torque applied on the axis of the hinge. This torque is assumed to have a restricted absolute value. A control law is constructed in the form of feedback along a single “unstable” coordinate of the open system in such a manner that the region of attraction of the linearized system would be the maximum possible. Several characteristic trajectories of the system for the control constructed are considered. |
| Received |
05 February 2016 |
| Link to Fulltext |
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