Author: Michael John CliffordPublisher:
ISBN:
Category :
Languages : en
Pages : 0
Book Description
The Parametrically Excited Pendulum
The Parametrically Excited Pendulum and the Criteria for Predicting the Onset of Chaos
Author: Tseng-Hsing HsuPublisher:
ISBN:
Category : Chaotic behavior in systems
Languages : en
Pages : 122
Book Description
Bifurcation Dynamics of a Damped Parametric Pendulum
Author: Yu GuoPublisher: Springer Nature
ISBN: 3031796454
Category : Technology & Engineering
Languages : en
Pages : 84
Book Description
The inherent complex dynamics of a parametrically excited pendulum is of great interest in nonlinear dynamics, which can help one better understand the complex world. Even though the parametrically excited pendulum is one of the simplest nonlinear systems, until now, complex motions in such a parametric pendulum cannot be achieved. In this book, the bifurcation dynamics of periodic motions to chaos in a damped, parametrically excited pendulum is discussed. Complete bifurcation trees of periodic motions to chaos in the parametrically excited pendulum include: period-1 motion (static equilibriums) to chaos, and period- motions to chaos ( = 1, 2, ···, 6, 8, ···, 12). The aforesaid bifurcation trees of periodic motions to chaos coexist in the same parameter ranges, which are very difficult to determine through traditional analysis. Harmonic frequency-amplitude characteristics of such bifurcation trees are also presented to show motion complexity and nonlinearity in such a parametrically excited pendulum system. The non-travelable and travelable periodic motions on the bifurcation trees are discovered. Through the bifurcation trees of travelable and non-travelable periodic motions, the travelable and non-travelable chaos in the parametrically excited pendulum can be achieved. Based on the traditional analysis, one cannot achieve the adequate solutions presented herein for periodic motions to chaos in the parametrically excited pendulum. The results in this book may cause one rethinking how to determine motion complexity in nonlinear dynamical systems.
The Parametrically Excited Pendulum System and Applications to Ship Dynamics
Author: Experimental Study of a Parametrically Excited Pendulum
Author: Fritz N. FrancisUnstable Periodic Orbits in the Parametrically Excited Pendulum
Author: van de Water (W.)Bifurcations and Chaos in a Parametrically Excited Double Pendulum
Author: A. C. SkeldonPublisher:
ISBN:
Category : Double pendulums
Languages : en
Pages : 312
Book Description
Autoparametric Resonance in Mechanical Systems
Author: Ales TondlPublisher: Cambridge University Press
ISBN: 9780521650793
Category : Science
Languages : en
Pages : 210
Book Description
Addresses the causes of and possible solutions to autoparametric resonance in mechanical systems.
Dynamics and Stability of Parametrically Excited Oscillators
Author: Richard Alan MorrisonMathematics of Complexity and Dynamical Systems
Author: Robert A. MeyersPublisher: Springer Science & Business Media
ISBN: 1461418054
Category : Mathematics
Languages : en
Pages : 1885
Book Description
Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics. Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely deterministic. The more than 100 entries in this wide-ranging, single source work provide a comprehensive explication of the theory and applications of mathematical complexity, covering ergodic theory, fractals and multifractals, dynamical systems, perturbation theory, solitons, systems and control theory, and related topics. Mathematics of Complexity and Dynamical Systems is an essential reference for all those interested in mathematical complexity, from undergraduate and graduate students up through professional researchers.