Author:
Kryzhevich Sergey,Plakhov Alexander
Abstract
AbstractThe 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.
Funder
Politechnika Gdańska
Center for Research and Development in Mathematics and Applications
Publisher
Springer Science and Business Media LLC
Subject
Control and Optimization,Numerical Analysis,Algebra and Number Theory,Control and Systems Engineering
Cited by
2 articles.
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1. Rotating rod and ball;Journal of Mathematical Analysis and Applications;2024-05
2. Dynamics of a Pendulum in a Rarefied Flow;Regular and Chaotic Dynamics;2024-01