On the structure of Hamiltonian impact systems

M. Pnueli, V. Rom-Kedar

Research output: Contribution to journalArticlepeer-review

Abstract

Tools for analyzing dynamics in a class of 2 degrees-of-freedom Hamiltonian impact systems with underlying separable integrable structure are derived. Integrable, near-integrable and far-from integrable cases are considered. In particular, a generalization of the energy momentum bifurcation diagram, Fomenko graphs and the hierarchy of bifurcations framework to this class is constructed. The projection of Liouville leaves of the smooth integrable dynamics to the configuration space allows to extend these tools to impact surfaces which produce far from integrable dynamics. It is suggested that such representations classify dynamically different regions in phase space. For the integrable and near integrable cases these provide global information on the dynamics whereas for the far from integrable regimes (caused by finite deformations of the impact surface), these provide information on the singular set and on the non-impact orbits. The results are presented and demonstrated for theDuffing-center system with impacts from a slanted wall.

Original languageEnglish
Pages (from-to)2611-2658
Number of pages48
JournalNonlinearity
Volume34
Issue number4
DOIs
StatePublished - Apr 2021

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • General Physics and Astronomy
  • Applied Mathematics

Fingerprint

Dive into the research topics of 'On the structure of Hamiltonian impact systems'. Together they form a unique fingerprint.

Cite this