scholarly journals Ship's Rolling Motion Analysis from the Nonlinear Dynamics Point of View-I : Poincare Mapping in Rolling Motion

1989 ◽  
Vol 81 (0) ◽  
pp. 117-124
Author(s):  
Rihei KAWASHIMA
Keyword(s):  
Nonlinear Dynamics ◽  
Motion Analysis ◽  
Point Of View ◽  
Rolling Motion ◽  
Poincaré Mapping ◽  
Poincare Mapping

Investigations of Stochastic Layers in Nonlinear Dynamics

1999 ◽  
Vol 122 (1) ◽  
pp. 36-41 ◽  
Author(s):  
Albert C. J. Luo ◽  
Ray P. S. Han
Keyword(s):  
Nonlinear Dynamics ◽  
Numerical Investigation ◽  
Duffing Oscillator ◽  
Minimum Energy ◽  
Energy Approach ◽  
Energy Spectra ◽  
Poincaré Mapping ◽  
Periodically Driven ◽  
Poincare Mapping ◽  
Stochastic Layer

The onset of a new resonance in the stochastic layer is predicted numerically through the maximum and minimum energy spectra when the energy jump in the spectra occurs. The incremental energy approach among all the established, analytic approaches gives the best prediction of the onset of resonance in the stochastic layer compared to numerical investigation. The stochastic layers in the periodically-driven pendulum are discussed as another example. Illustrations of stochastic layers in the twin-well Duffing oscillator and the periodically-driven pendulum are given through the Poincare´ mapping sections. [S0739-3717(00)00701-7]

scholarly journals An Improved Method for Estimating the Domain of Attraction of Passive Biped Walker

2019 ◽  
Vol 2019 ◽  
pp. 1-11 ◽  
Author(s):  
Yu Wang ◽  
Heng Cao ◽  
JinLin Jiang
Keyword(s):  
Domain Of Attraction ◽  
Mapping Method ◽  
Simple Cell ◽  
Iteration Algorithm ◽  
Poincaré Mapping ◽  
Cell Mapping ◽  
Improved Method ◽  
Stable Domain ◽  
Simple Cell Mapping ◽  
Poincare Mapping

An indicator of a passive biped walker’s global stability is its domain of attraction, which is usually estimated by the simple cell mapping method. It needs to calculate a large number of cells’ Poincare mapping result in the estimating process. However, the Poincare mapping is usually computationally expensive and time-consuming due to the complex dynamical equation of the passive biped walker. How to estimate the domain of attraction efficiently and reliably is a problem to be solved. Based on the simple cell mapping method, an improved method is proposed to solve it. The proposed method uses the multiple iteration algorithm to calculate a stable domain of attraction and effectively decreases the total number of Poincare mappings. Through the simulation of the simplest passive biped walker, the improved method can obtain the same domain of attraction as that calculated using the simple cell mapping method and reduce calculation time significantly. Furthermore, this improved method not only proposes a way of rapid estimating the domain of attraction, but also provides a feasible tool for selecting the domain of interest and its discretization level.

scholarly journals Study on Clearance-Rubbing Dynamic Behavior of 2-DOF Supporting System of Magnetic-Liquid Double Suspension Bearing

Processes ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 973
Author(s):  
Jianhua Zhao ◽  
Weidong Yan ◽  
Ziqi Wang ◽  
Dianrong Gao ◽  
Guojun Du
Keyword(s):  
Stable Operation ◽  
Poincaré Mapping ◽  
Eccentricity Ratio ◽  
Magnetic Liquid ◽  
Rotating Speed ◽  
Single Period ◽  
Operating Stability ◽  
Poincare Mapping ◽  
Assembly Error ◽  
Mapping Point

As a new type of suspension bearing, Magnetic-Liquid Double Suspension Bearing (MLDSB) is mainly supported by electromagnetic suspension and supplemented by hydrostatic supporting. Its bearing capacity and stiffness can be greatly improved. Because of the small liquid film thickness (it is smaller 10 times than air gap), the eccentricity, crack, bending of the rotor, and the assembly error, it is easy to cause a clearance-rubbing fault between the rotor and stator. The coating can be worn and peeled, the operating stability can be reduced, and then it is one of the key problems of restricting the development and application of MLDSB. Therefore, the clearance-rubbing dynamic equation of 2-DOF system of MLDSB is established and converted into Taylor Series form and the nonlinear components are retained. Dimensionless treatment is carried out by dimensional normalization method. Finally, the rotor displacement response under different rotor eccentricity ratio and rotating speeds is numerically simulated. The studies show that the trajectory of the rotor is periodic elliptic without clearance-rubbing phenomenon when the eccentricity ratio is less than 0.2, while the rotor is greatly affected by the rotation speed and a variety of motions, such as single-period, quasi-period, double-period and chaos, are presented when greater than 0.3. Within the largest range of rotating speed and eccentricity ratio, the rotor presents the single-period trajectory, and then the number of Poincare mapping point is 1, without a clearance-rubbing fault. When the rotational speed is in the scope of (9, 13) krpm and the eccentricity ratio is in the scope of (0.27, 0.4), the number of Poincare mapping point is more than one, the maximum dimensionless rubbing force is −5.7, and then clearance-rubbing fault occurs. The research can provide a theoretical basis for the safe and stable operation of MLDSB.

scholarly journals Motion analysis for the evaluation of muscle overactivity: A point of view

2019 ◽  
Vol 62 (6) ◽  
pp. 442-452 ◽  
Author(s):  
N. Roche ◽  
C. Bonnyaud ◽  
V. Reynaud ◽  
D. Bensmail ◽  
D. Pradon ◽  
...  
Keyword(s):  
Motion Analysis ◽  
Point Of View

Optical properties and Poincaré mapping in spherical multilayered systems: periodic, quasiperiodic, and disordered

2014 ◽  
Vol 38 (10) ◽  
pp. 2027-2034
Author(s):  
A. Díaz-de-Anda ◽  
M. Nájera-Villeda ◽  
Gennadiy Burlak ◽  
A. Zamudio-Lara
Keyword(s):  
Optical Properties ◽  
Poincaré Mapping ◽  
Poincare Mapping ◽  
Multilayered Systems
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