2016/01/01 by Wojciech Szumiński, Tomasz Stachowiak · 1 citation
Computer Science · Engineering · Physics and Astronomy · #Contact Mechanics and Variational Inequalities #Dynamics (music) #Equilibrium point #Linear system #Motion (physics) #Quantum chaos and dynamical systems #Spacecraft Dynamics and Control #Stability (learning theory) #nlin.CD
paper · pdf · doi:10.1007/978-3-319-42408-8_29
published as Applied Non-Linear Dynamical Systems, ed. Jan Awrejcewicz, Springer Proceedings in Mathematics & Statistics 182, pp. 361-372, 2016
openalex publication_date 2016/01/01 · arxiv created 2016/10/21 · arxiv updated 2016/10/24 · openalex created_date 2016/11/04 · openalex updated_date 2026/08/05
We consider the system of two material points that interact by elastic forces according to Hooke's law and their motion is restricted to certain curves lying on the plane. The nonintegrability of this system and idea of the proof are communicated. Moreover, the analysis of global dynamics by means of Poincaré cross sections is given and local analysis in the neighborhood of an equilibrium is performed by applying the Birkhoff normal form. Conditions of linear stability are determined and some particular periodic solutions are identified.