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Dynamics of bouncing convex body.
- Source :
-
Chaos, Solitons & Fractals . Jun2024, Vol. 183, pN.PAG-N.PAG. 1p. - Publication Year :
- 2024
-
Abstract
- We consider a dynamical system that describes a convex planer body with a smooth boundary, which falls under the influence of gravity and is elastically reflected upon hitting a wall. Under suitable restriction on the system's parameters, the system is equivalent to a billiard problem within a cylinder. We prove that the dynamics of the system is intimately linked to a variational problem, corresponding to a twist map. Moreover, we utilise the established variational method to investigate the stability of trivial periodic orbits and near-integrable dynamics when this planar body closely approximates a disc with its centre of mass at the geometric centre. Numerical results illustrates our mathematical findings and highlight the system's intricate dynamics. [ABSTRACT FROM AUTHOR]
- Subjects :
- *DYNAMICAL systems
*ORBITS (Astronomy)
*SYSTEM dynamics
*CONVEX bodies
Subjects
Details
- Language :
- English
- ISSN :
- 09600779
- Volume :
- 183
- Database :
- Academic Search Index
- Journal :
- Chaos, Solitons & Fractals
- Publication Type :
- Periodical
- Accession number :
- 177315891
- Full Text :
- https://doi.org/10.1016/j.chaos.2024.114895