کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
8052493 1519393 2016 16 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Deterministic and stochastic aspects of the stability in an inverted pendulum under a generalized parametric excitation
ترجمه فارسی عنوان
جنبه های قطعی و تصادفی ثبات در یک آونگ معکوس تحت یک تحریک پارامتر عمومی
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه سایر رشته های مهندسی مکانیک محاسباتی
چکیده انگلیسی
In this paper, we explore the stability of an inverted pendulum under a generalized parametric excitation described by a superposition of N cosines with different amplitudes and frequencies, based on a simple stability condition that does not require any use of Lyapunov exponent, for example. Our analysis is separated in 3 different cases: N=1,N=2, and N very large. Our results were obtained via numerical simulations by fourth-order Runge-Kutta integration of the non-linear equations. We also calculate the effective potential also for N > 2. We show then that numerical integrations recover a wider region of stability that are not captured by the (approximated) analytical method of the effective potential. We also analyze stochastic stabilization here: firstly, we look the effects of external noise in the stability diagram by enlarging the variance, and secondly, when N is large, we rescale the amplitude by showing that the diagrams for survival time of the inverted pendulum resembles the exact case for N=1. Finally, we find numerically the optimal number of cosines corresponding to the maximal survival probability of the pendulum.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied Mathematical Modelling - Volume 40, Issues 23–24, December 2016, Pages 10689-10704
نویسندگان
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