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ЖУРНАЛЫ // Regular and Chaotic Dynamics // Архив

Regul. Chaotic Dyn., 2020, том 25, выпуск 6, страницы 729–752 (Mi rcd1096)

Эта публикация цитируется в 13 статьях

Stability and Stabilization of Steady Rotations of a Spherical Robot on a Vibrating Base

Alexander A. Kilin, Elena N. Pivovarova

Ural Mathematical Center, Udmurt State University, ul. Universitetskaya 1, 426034 Izhevsk, Russia

Аннотация: This paper addresses the problem of a spherical robot having an axisymmetric pendulum drive and rolling without slipping on a vibrating plane. It is shown that this system admits partial solutions (steady rotations) for which the pendulum rotates about its vertical symmetry axis. Special attention is given to problems of stability and stabilization of these solutions. An analysis of the constraint reaction is performed, and parameter regions are identified in which a stabilization of the spherical robot is possible without it losing contact with the plane. It is shown that the partial solutions can be stabilized by varying the angular velocity of rotation of the pendulum about its symmetry axis, and that the rotation of the pendulum is a necessary condition for stabilization without the robot losing contact with the plane.

Ключевые слова: spherical robot, vibrations, stability, stabilization, partial solutions, constraint reaction, Lagrange top, Kapitsa pendulum.

MSC: 70E18, 37J60, 70E50, 34H15

Поступила в редакцию: 19.09.2020
Принята в печать: 13.11.2020

Язык публикации: английский

DOI: 10.1134/S1560354720060155



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