2007/06/02 by Andrzej Okniński, Andrzej Okninski, Okninski, Andrzej +3 · 1 citation
Engineering · Mathematics · Physics and Astronomy · #70F35 #Advanced Differential Equations and Dynamical Systems #Advanced Differential Geometry Research #Chaotic Dynamics (nlin.CD) #Elasticity and Wave Propagation #FOS: Physical sciences #Quantum chaos and dynamical systems #msc:70F35 #nlin.CD
paper · pdf · doi:10.48550/arxiv.0706.0257
LaTeX, 17 pages, 5 figures (integrated with the text)
openalex publication_date 2007/06/02 · arxiv created 2012/12/26 · arxiv updated 2012/12/27 · openalex created_date 2022/09/03 · openalex updated_date 2026/07/28
Dynamics near the grazing manifold and basins of attraction for a motion of a material point in a gravitational field, colliding with a moving motion-limiting stop, are investigated. The Poincare map, describing evolution from an impact to the next impact, is derived. Periodic points are found and their stability is determined. The grazing manifold is computed and dynamics is approximated in its vicinity. It is shown that on the grazing manifold there are trapping as well as forbidden regions. Finally, basins of attraction are studied.