Abstract
Periodic motions in a discontinuous dynamical system are studied. The discontinuous dynamical system consists of three distinct linear dynamical systems with two different circular boundaries. Analytical conditions for switching and sliding motions at the two circular boundaries are developed. From such analytical conditions, periodic motions in discontinuous dynamical systems can be determined through specific mapping structures. Illustrations give periodic motions in discontinuous dynamical systems, which are different from the continuous dynamical systems. In different domains, the motions are different, and the discontinuity of the periodic motions at the boundaries is observed, and the sliding motion on the boundaries is also a portion of periodic motion. Such periodic motions in discontinuous dynamical systems do not have any Fourier series. The methodology presented in this paper can be applied to other discontinuous dynamical systems. The circular boundaries can be treated different energy levels as control conditions in engineering systems.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
