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Abstract
We consider a mechanical 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. The ball is reflected elastically when colliding with the rod and moves freely between consecutive hits. A sliding motion along the rod is also allowed. We prove the existence and uniqueness of the motion with a given position and velocity at a certain time instant. We prove that only 5 kinds of motion are possible: a billiard motion; a sliding motion; a billiard motion followed by sliding; a sliding motion followed by a billiard one; and a constant motion when the ball is at the center of rotation. The asymptotic behaviors of time intervals between consecutive hits and of distances between the points of hits on the rod are determined.
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Authors (2)
-
Alexander Plakhov prof.
- Universidade de Aveiro
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Keywords
Details
- Category:
- Articles
- Type:
- artykuły w czasopismach
- Published in:
-
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
no. 533,
ISSN: 0022-247X - Language:
- English
- Publication year:
- 2024
- Bibliographic description:
- Kryzhevich S., Plakhov A.: Rotating rod and ball// JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS -,iss. 3 (2024),
- DOI:
- Digital Object Identifier (open in new tab) 10.1016/j.jmaa.2023.128018
- Sources of funding:
-
- IDUB
- Verified by:
- Gdańsk University of Technology
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