Analysis of a Constrained Two-Body Problem
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.
The work has been supported by grants No. DEC-2013/09/B/ST1/ 04130 and DEC-2011/02/A/ST1/00208 of National Science Centre of Poland.
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