Controllability of the Ishlinsky system

Authors

  • Alexand S. Kulesh Lomonosov Moscow State University, GSP-1, Leninskie Gory, 1, Moscow, 119991, Russian Federation;
  • Vadim V. Rybin Lomonosov Moscow State University, GSP-1, Leninskie Gory, 1, Moscow, 119991, Russian Federation;

Abstract

In 1965 A. Yu. Ishlinsky proposed the example of a low dimensional nonholonomic non-Chaplygin mechanical system. The Ishlinsky system consists of three cylinders. One of them with the radius R rolls without sliding on top of two other identical cylinders of a radius a, which each roll whithout sliding on a fixed horizontal plane. In this paper we analyze controllability conditions for the system of cylinders. We prove that the Ishlinsky system is completely controllable by the Chow – Rashevsky theorem. This example of a non-Chaplygin nonholonomic system clearly illustrates the analytic and control coplexity of such systems. Refs 3. Figs

Keywords:

nonholonomic system, rolling without sliding, controllability

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Published

2014-05-01

How to Cite

Kulesh, A. S., & Rybin, V. V. (2014). Controllability of the Ishlinsky system. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 1(2), 278–283. Retrieved from https://math-mech-astr-journal.spbu.ru/article/view/11053

Issue

Vol. 1 No. 2 (2014)

Section

Mechanics

License

Articles of "Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.