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Abstract
The main objective of this research is to study the properties of a billiard system in an unbounded domain with moving boundary. We consider a system consisting of an infinite rod (a straight line) and a ball (a massless point) on the plane. The rod rotates uniformly around one of its points and experiences elastic collisions with the ball. We define a mathematical model for the dynamics of such a system and write down asymptotic formulae for its motions. In particular, we determine existence and uniqueness of solutions. We find all possible grazing impacts of the ball. Besides, we demonstrate that for almost every initial condition, the ball goes to infinity exponentially fast, with the time intervals between neighboring collisions tending to zero. The approach developed in this paper is an original combination of methods of Billiards and Vibro-Impact Dynamics. It could be a base for studying more complicated systems of similar types.
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Authors (2)
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Alexander Plakhov prof.
- Universidade de Aveiro
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Full text
- Publication version
- Accepted or Published Version
- DOI:
- Digital Object Identifier (open in new tab) 10.1007/s10883-023-09655-z
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Details
- Category:
- Articles
- Type:
- artykuły w czasopismach
- Published in:
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JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS
no. 29,
pages 1695 - 1707,
ISSN: 1079-2724 - Language:
- English
- Publication year:
- 2023
- Bibliographic description:
- Kryzhevich S., Plakhov A.: Billiard in a rotating half-plane// JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS -, (2023), s.1695-1707
- DOI:
- Digital Object Identifier (open in new tab) 10.1007/s10883-023-09655-z
- Sources of funding:
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- IDUB
- Verified by:
- Gdańsk University of Technology
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