کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
8256494 1534035 2014 20 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
The scattering map in two coupled piecewise-smooth systems, with numerical application to rocking blocks
ترجمه فارسی عنوان
نقشه پراکندگی در دو سیستم یکپارچه و صاف، به همراه اعمال عددی به بلوک های شیب دار
کلمات کلیدی
انتشار آرنولد، سیستم های صاف و شفاف، بلوک روکش
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
چکیده انگلیسی
We consider a non-autonomous dynamical system formed by coupling two piecewise-smooth systems in R2 through a non-autonomous periodic perturbation. We study the dynamics around one of the heteroclinic orbits of one of the piecewise-smooth systems. In the unperturbed case, the system possesses two C0 normally hyperbolic invariant manifolds of dimension two with a couple of three dimensional heteroclinic manifolds between them. These heteroclinic manifolds are foliated by heteroclinic connections between C0 tori located at the same energy levels. By means of the impact map we prove the persistence of these objects under perturbation. In addition, we provide sufficient conditions of the existence of transversal heteroclinic intersections through the existence of simple zeros of Melnikov-like functions. The heteroclinic manifolds allow us to define the scattering map, which links asymptotic dynamics in the invariant manifolds through heteroclinic connections. First order properties of this map provide sufficient conditions for the asymptotic dynamics to be located in different energy levels in the perturbed invariant manifolds. Hence we have an essential tool for the construction of a heteroclinic skeleton which, when followed, can lead to the existence of Arnold diffusion: trajectories that, on large time scales, destabilize the system by further accumulating energy. We validate all the theoretical results with detailed numerical computations of a mechanical system with impacts, formed by the linkage of two rocking blocks with a spring.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Physica D: Nonlinear Phenomena - Volume 269, 15 February 2014, Pages 1-20
نویسندگان
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