On the Preservation of Conditionally Periodic Motions Under Small Variations of the Hamilton Function

1991 ◽  
pp. 349-354
Author(s):  
V. M. Tikhomirov
Keyword(s):  
Periodic Motions ◽  
Hamilton Function

Investigation of the stability of periodic motions in a nonlinear automatic control system based on the fast fourier transform

2003 ◽  
Vol 3 ◽  
pp. 297-307
Author(s):  
V.V. Denisov
Keyword(s):  
Fourier Transform ◽  
Control System ◽  
Automatic Control ◽  
Fast Fourier Transform ◽  
Automatic Control System ◽  
Resonance Phenomenon ◽  
Periodic Motions ◽  
Multiply Connected ◽  
Non Linear ◽  
The Stability

An approach to the study of the stability of non-linear multiply connected systems of automatic control by means of a fast Fourier transform and the resonance phenomenon is considered.

scholarly journals On excessive Transverse Coordinates for Orbital Stabilization of Periodic Motions

2020 ◽  
Vol 53 (2) ◽  
pp. 9250-9255
Author(s):  
Christian Fredrik Sætre ◽  
Anton Shiriaev
Keyword(s):  
Periodic Motions ◽  
Orbital Stabilization

On the Analysis of Hopf Bifurcation Associated with a Two-Fold Zero Eigenvalue, Part 1: Autonomous System

1999 ◽  
Vol 121 (1) ◽  
pp. 101-104 ◽  
Author(s):  
M. Moh’d ◽  
K. Huseyin
Keyword(s):  
Hopf Bifurcation ◽  
Limit Cycles ◽  
Autonomous System ◽  
Periodic Motions ◽  
Zero Eigenvalue ◽  
The Family ◽  
Dynamic Bifurcations ◽  
Formula Type

The static and dynamic bifurcations of an autonomous system associated with a twofold zero eigenvalue (of index one) are studied. Attention is focused on Hopf bifurcation solutions in the neighborhood of such a singularity. The family of limit cycles are analyzed fully by applying the formula type results of the Intrinsic Harmonic Balancing method. Thus, parameter-amplitude and amplitude-frequency relationships as well as an ordered form of approximations for the periodic motions are obtained explicitly. A verification technique, with the aid of MAPLE, is used to show the consistency of ordered approximations.

LSTM-based approach for predicting periodic motions of an impacting system via transient dynamics

2021 ◽  
Author(s):  
Kenneth Omokhagbo Afebu ◽  
Yang Liu ◽  
Evangelos Papatheou ◽  
Bingyong Guo
Keyword(s):  
Transient Dynamics ◽  
Periodic Motions

The analysis of TWI data for human being's periodic motions

2011 ◽  
Author(s):  
Zhaofa Zeng ◽  
Jiguang Sun ◽  
Jing Li ◽  
Fengshan Liu ◽  
Qi Lu ◽  
...  
Keyword(s):  
Periodic Motions

Bifurcation Trees of Periodic Motions to Chaos in a Parametric, Quadratic Nonlinear Oscillator

2014 ◽  
Vol 24 (05) ◽  
pp. 1450075 ◽  
Author(s):  
Albert C. J. Luo ◽  
Bo Yu
Keyword(s):  
Fourier Series ◽  
Nonlinear Systems ◽  
Analytical Solutions ◽  
Nonlinear Oscillator ◽  
Series Solution ◽  
Parametric Oscillator ◽  
Periodic Motions ◽  
Parametric Oscillators ◽  
Harmonic Term ◽  
Nonlinear Behaviors

In this paper, bifurcation trees of periodic motions to chaos in a parametric oscillator with quadratic nonlinearity are investigated analytically as one of the simplest parametric oscillators. The analytical solutions of periodic motions in such a parametric oscillator are determined through the finite Fourier series, and the corresponding stability and bifurcation analyses for periodic motions are completed. Nonlinear behaviors of such periodic motions are characterized through frequency–amplitude curves of each harmonic term in the finite Fourier series solution. From bifurcation analysis of the analytical solutions, the bifurcation trees of periodic motion to chaos are obtained analytically, and numerical illustrations of periodic motions are presented through phase trajectories and analytical spectrum. This investigation shows period-1 motions exist in parametric nonlinear systems and the corresponding bifurcation trees to chaos exist as well.

scholarly journals On the periodic motions of dynamical systems

1927 ◽  
Vol 50 (0) ◽  
pp. 359-379 ◽  
Author(s):  
George D. Birkhoff
Keyword(s):  
Dynamical Systems ◽  
Periodic Motions

Analysis of Bifurcations for a Functionally Graded Materials Plate

2013 ◽  
Vol 300-301 ◽  
pp. 988-991 ◽  
Author(s):  
Wei Qin Yu
Keyword(s):  
Functionally Graded Materials ◽  
Functionally Graded ◽  
Periodic Motions ◽  
Graded Materials ◽  
Normal Form Theory ◽  
Closed Form Solutions ◽  
Simply Supported ◽  
Form Theory ◽  
Bifurcation And Stability ◽  
Numerical Approaches

Using the analytical and numerical approaches, the nonlinear dynamic behaviors in the vicinity of a compound critical point are studied for a simply supported functionally graded materials (FGMs) rectangular plate. Normal form theory, bifurcation and stability theory are used to find closed form solutions for equilibria and periodic motions. Stability conditions of these solutions are obtained explicitly and critical boundaries are also derived. Finally, numerical results are presented to confirm the analytical predictions

Galloping Vibration of Nonlinear Cables Through a Two Degree-of-Freedom Oscillator

2016 ◽  
Author(s):  
Albert C. J. Luo ◽  
Bo Yu
Keyword(s):  
Transmission Line ◽  
Analytical Solutions ◽  
Transmission Lines ◽  
Nonlinear Oscillator ◽  
Numerical Solutions ◽  
Degree Of Freedom ◽  
Periodic Motions ◽  
Stability And Bifurcation ◽  
Two Degree Of Freedom

In this paper, galloping vibrations of a lightly iced transmission line are investigated through a two-degree-of-freedom (2-DOF) nonlinear oscillator. The 2-DOF nonlinear oscillator is used to describe the transverse and torsional motions of the galloping cables. The analytical solutions of periodic motions of galloping cables are presented through generalized harmonic balanced method. The analytical solutions of periodic motions for the galloping cable are compared with the numerical solutions, and the corresponding stability and bifurcation of periodic motions are analyzed by the eigenvalues analysis. To demonstrate the accuracy of the analytical solutions of periodic motions, the harmonic amplitudes are presented. This investigation will help one better understand galloping mechanism of iced transmission lines.

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