On the non-integrability and dynamics of discrete models of threads
Abstract
In the paper, we study the dynamics of planar n-gons, which can be considered as discrete models of threads. The main result of the paper is that, under some weak assumptions, these systems are not integrable in the sense of Liouville. This holds for both completely free threads and for threads with fixed points that are placed in external force fields. We present sufficient conditions for the positivity of topological entropy in such systems. We briefly consider other dynamical properties of discrete threads and we also consider discrete models of inextensible yet compressible threads.
- Publication:
-
Nonlinearity
- Pub Date:
- September 2021
- DOI:
- 10.1088/1361-6544/ac1559
- arXiv:
- arXiv:2009.09517
- Bibcode:
- 2021Nonli..34.6398K
- Keywords:
-
- inextensible thread;
- non-integrability;
- topological entropy;
- discrete model;
- planar linkage;
- 37J30;
- Nonlinear Sciences - Chaotic Dynamics
- E-Print:
- doi:10.1088/1361-6544/ac1559