The Existence of Q-Rotaing Periodic Solutions for Second Order Nonlinear Dynamical Systems

2016 ◽  
Author(s):  
Bingyu Kou ◽  
Pu Wang ◽  
Lei Mao ◽  
Xinghu Teng
Keyword(s):  
Dynamical Systems ◽  
Periodic Solutions ◽  
Nonlinear Dynamical Systems ◽  
Second Order ◽  
Nonlinear Dynamical

Prediction for the Rub-Impact Phenomena in Rotor Systems

2001 ◽  
Author(s):  
Zhiqiang Wu ◽  
Yushu Chen
Keyword(s):  
Dynamical Systems ◽  
Periodic Solutions ◽  
Nonlinear Dynamical Systems ◽  
Nonlinear Dynamical ◽  
Rotor Systems ◽  
Different Types ◽  
Impact Phenomena ◽  
Direct Guidance

Abstract By the method (Wu, 2001) developed by authors for singularity analyzing of the bifurcation of the periodic solutions in nonlinear dynamical systems with clearance, the bifurcation patterns of non-impact-rub response and a method for predicting rub-impact are given. It is shown that there are much more types of bifurcation patterns when the clearance constraint is take into account. Given their physical meanings of the parameters in practical rotor systems, the resonant periodic solutions of rotor systems consist of 11 different types of bifurcation patterns among of which the following four types are more likely to appear, (1) patterns without impact and jump, (2) jump patterns without impact, (3) impact pattern without jump and (4) patterns with impact and jump. Based on these results, parameter conditions for rub-impact phenomena are derived. These conditions can give more direct guidance to the design of rotor systems. The method proposed here can be used to predict rub-impact phenomena in more complicated rotor systems.

A Terminal Sliding Mode Control of Disturbed Nonlinear Second-Order Dynamical Systems

2016 ◽  
Vol 11 (5) ◽  
Author(s):  
Pawel Skruch
Keyword(s):  
Dynamical Systems ◽  
Nonlinear Dynamical Systems ◽  
Sliding Mode ◽  
Second Order ◽  
Control Law ◽  
Sliding Surface ◽  
Terminal Sliding Mode ◽  
Nonlinear Dynamical ◽  
Second Order Differential Equations ◽  
Bounded Disturbance

The paper presents a terminal sliding mode controller for a certain class of disturbed nonlinear dynamical systems. The class of such systems is described by nonlinear second-order differential equations with an unknown and bounded disturbance. A sliding surface is defined by the system state and the desired trajectory. The control law is designed to force the trajectory of the system from any initial condition to the sliding surface within a finite time. The trajectory of the system after reaching the sliding surface remains on it. A computer simulation is included as an example to verify the approach and to demonstrate its effectiveness.

The Necessary Condition for the Existence of Periodic Solutions of Certain Three Dimensional Nonlinear Dynamical Systems

2012 ◽  
Vol 252 ◽  
pp. 40-43
Author(s):  
Ting Ting Quan ◽  
Jing Li ◽  
Min Sun
Keyword(s):  
Dynamical Systems ◽  
Periodic Solutions ◽  
Nonlinear Dynamical Systems ◽  
Three Dimensional ◽  
Basic Research ◽  
Necessary Condition ◽  
Nonlinear Dynamical ◽  
Closed Orbits ◽  
Existence Of Periodic Solutions ◽  
Important Significance

In this paper, we investigate a class of three dimensional nonlinear dynamical systems whose unperturbed systems have a family of periodic orbits. Firstly, we establish the moving Frenet Frame on these closed orbits. Secondly, the successor functions are defined by the orbits which go through the normal plane. Finally, by judging the existence of solutions of the equations obtained from the Successor functions, we obtain the necessary condition for the existence of periodic solutions of these three dimensional nonlinear dynamical systems. The result has important significance for the basic research of applied mechanics.

SYNCHRONIZATION OF A CLASS OF SECOND-ORDER NONLINEAR SYSTEMS

2008 ◽  
Vol 18 (11) ◽  
pp. 3461-3471 ◽  
Author(s):  
A. P. MIJOLARO ◽  
L. F. C. ABERTO ◽  
N. G. BRETAS
Keyword(s):  
Asymptotic Behavior ◽  
Vector Field ◽  
Dynamical Systems ◽  
Nonlinear Dynamical Systems ◽  
Second Order ◽  
Coupled Systems ◽  
Nonlinear Dynamical ◽  
Unbounded Solutions ◽  
Synchronization Region ◽  
Coupling Parameters

The asymptotic behavior of a class of coupled second-order nonlinear dynamical systems is studied in this paper. Using very mild assumptions on the vector-field, conditions on the coupling parameters that guarantee synchronization are provided. The proposed result does not require solutions to be ultimately bounded in order to prove synchronization, therefore it can be used to study coupled systems that do not globally synchronize, including synchronization of unbounded solutions. In this case, estimates of the synchronization region are obtained. Synchronization of two-coupled nonlinear pendulums and two-coupled Duffing systems are studied to illustrate the application of the proposed theory.

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