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Russian Academy of Sciences
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IssuesArchive of Issues2016-4pp.316-323

Archive of Issues

Total articles in the database: 1813
In Russian (): 1014
In English (J. Appl. Math. Mech.): 799

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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 5 February 2016
Link to Fulltext http://www.sciencedirect.com/science/article/pii/S002189281630123X
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