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The global stability of two-dimensional systems for controlling angular orientation

Authors
Journal
Journal of Applied Mathematics and Mechanics
0021-8928
Publisher
Elsevier
Publication Date
Volume
64
Issue
5
Identifiers
DOI: 10.1016/s0021-8928(00)00113-1
Disciplines
  • Mathematics

Abstract

Abstract A two-dimensional dynamic system with an angular coordinate, describing the operation of a two-position automatic steering device, the plane rotations of a spacecraft controlled by an angular orientation system, and phase-lock control frequency system with a proportional-plus-integral filter is considered. An analogue of the Barbashin-Krasovskii theorem is obtained for differential inclusions with angular coordinates. This is used to prove the global stability of two-dimensional systems of angular orientation when there is no external force moment. It is shown that, when there is a constant external force moment in phase space, a region of initial conditions exists that corresponds to circular motions of a spacecraft.

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