A direct analysis of nonlinear systems with external periodic excitations via normal forms

2008 ◽  
Vol 55 (1-2) ◽  
pp. 79-93 ◽  
Author(s):  
Amit P. Gabale ◽  
S. C. Sinha
Keyword(s):  
Nonlinear Systems ◽  
Normal Forms ◽  
Direct Analysis

A New Approach for Computing the Normal Forms of High Dimensional Nonlinear Systems

2010 ◽  
Author(s):  
Shuping Chen ◽  
Wei Zhang ◽  
Minghui Yao
Keyword(s):  
Nonlinear Systems ◽  
Normal Form ◽  
Cantilever Beam ◽  
Normal Forms ◽  
Nonlinear Differential Equations ◽  
Real Life ◽  
High Dimensional ◽  
Computation Method ◽  
Normal Form Theory ◽  
Averaged Equations

Normal form theory is very useful for direct bifurcation and stability analysis of nonlinear differential equations modeled in real life. This paper develops a new computation method for obtaining a significant refinement of the normal forms for high dimensional nonlinear systems. The method developed here uses the lower order nonlinear terms in the normal form for the simplifications of higher order terms. In the theoretical model for the nonplanar nonlinear oscillation of a cantilever beam, the computation method is applied to compute the coefficients of the normal forms for the case of two non-semisimple double zero eigenvalues. The normal forms of the averaged equations and their coefficients for non-planar non-linear oscillations of the cantilever beam under combined parametric and forcing excitations are calculated.

Observer normal forms for a class of nonlinear systems by means of coupled auxiliary dynamics

2020 ◽  
Vol 30 (13) ◽  
pp. 4960-4978
Author(s):  
Li‐Fei Wang ◽  
Driss Boutat ◽  
Da‐Yan Liu
Keyword(s):  
Nonlinear Systems ◽  
Normal Forms

Lucid Analysis of Periodically Forced Nonlinear Systems via Normal Forms

2019 ◽  
Author(s):  
Peter M. B. Waswa ◽  
Sangram Redkar
Keyword(s):  
Nonlinear Systems ◽  
Ad Hoc ◽  
Normal Forms ◽  
Numerical Results ◽  
Duffing Equation ◽  
System State ◽  
Periodic Forcing ◽  
Periodic Coefficients ◽  
Duffing’S Equation ◽  
State Augmentation

Abstract This paper presents a straightforward methodology to analyze periodically forced nonlinear systems with constant and periodic coefficients via normal forms. We demonstrate how the intuitive system state augmentation facilitates construction of normal forms by avoiding ad-hoc addition of equation variables, book-keeping parameters and detuning parameters. Moreover, this technique directly connects the periodic forcing terms and periodic coefficients of the nonlinearity with the augmented states — making it applicable to all periodically forced nonlinear systems. Accuracy of this approach is successfully verified via fulfilled compliance between analytical and numerical results of forced Duffing’s equation and Mathieu-Duffing equation.

Computation of Normal Forms of Bogdanov-Takens Singularities for High Dimensional Nonlinear Systems

2010 ◽  
Author(s):  
Shuping Chen ◽  
Wei Zhang ◽  
Youhua Qian ◽  
Jane W. Z. Lu ◽  
Andrew Y. T. Leung ◽  
...  
Keyword(s):  
Nonlinear Systems ◽  
Normal Forms ◽  
High Dimensional

On Normal Forms of Nonlinear Systems Affine in Control

2011 ◽  
Vol 56 (2) ◽  
pp. 239-253 ◽  
Author(s):  
Xinmin Liu ◽  
Zongli Lin
Keyword(s):  
Nonlinear Systems ◽  
Normal Forms
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