Approximate first integrals of nonlinear oscillators with one-degree of freedom

ARI ◽  
1999 ◽  
Vol 51 (4) ◽  
pp. 258-267
Author(s):  
G. Ünal ◽  
A. Kırış
Keyword(s):  
Nonlinear Oscillators ◽  
First Integrals ◽  
Degree Of Freedom ◽  
Approximate First Integrals

Performance analysis of global local mean square error criterion of stochastic linearization for nonlinear oscillator

2019 ◽  
Author(s):  
Nguyen Cao Thang ◽  
Luu Xuan Hung
Keyword(s):  
Performance Analysis ◽  
Mean Square Error ◽  
Nonlinear Oscillators ◽  
Degree Of Freedom ◽  
Equivalent Linearization ◽  
Mean Square ◽  
Error Criterion ◽  
Stochastic Linearization ◽  
Local Mean ◽  
Mean Square Error Criterion

The paper presents a performance analysis of global-local mean square error criterion of stochastic linearization for some nonlinear oscillators. This criterion of stochastic linearization for nonlinear oscillators bases on dual conception to the local mean square error criterion (LOMSEC). The algorithm is generally built to multi degree of freedom (MDOF) nonlinear oscillators. Then, the performance analysis is carried out for two applications which comprise a rolling ship oscillation and two degree of freedom one. The improvement on accuracy of the proposed criterion has been shown in comparison with the conventional Gaussian equivalent linearization (GEL).

An Observation on Least Action Principle in Classical Mechanics Oriented on the Evaluation of Relativistic Error Concerning the Measurements of Light Propagating in a Liquid

2011 ◽  
Vol 1 (3) ◽  
pp. 14-24 ◽  
Author(s):  
Alessandro Massaro ◽  
Piero Adriano Massaro
Keyword(s):  
Euler Equations ◽  
Classical Mechanics ◽  
First Integrals ◽  
Action Principle ◽  
Classical Approach ◽  
Limit Case ◽  
Least Action Principle ◽  
Calculus Of Variation ◽  
Least Action ◽  
Approximate First Integrals

The authors prove that the standard least action principle implies a more general form of the same principle by which they can state generalized motion equation including the classical Euler equation as a particular case. This form is based on an observation regarding the last action principle about the limit case in the classical approach using symmetry violations. Furthermore the well known first integrals of the classical Euler equations become only approximate first integrals. The authors also prove a generalization of the fundamental lemma of the calculus of variation and we consider the application in electromagnetism.

scholarly journals On the critical forcing amplitude of forced nonlinear oscillators

2013 ◽  
Vol 3 (4) ◽  
Author(s):  
Mariano Febbo ◽  
Jinchen Ji
Keyword(s):  
Primary Resonance ◽  
Nonlinear Oscillators ◽  
Analytical Form ◽  
Excitation Amplitude ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Weakly Nonlinear ◽  
Single Degree ◽  
Saddle Node ◽  
Basis Method

AbstractThe steady-state response of forced single degree-of-freedom weakly nonlinear oscillators under primary resonance conditions can exhibit saddle-node bifurcations, jump and hysteresis phenomena, if the amplitude of the excitation exceeds a certain value. This critical value of excitation amplitude or critical forcing amplitude plays an important role in determining the occurrence of saddle-node bifurcations in the frequency-response curve. This work develops an alternative method to determine the critical forcing amplitude for single degree-of-freedom nonlinear oscillators. Based on Lagrange multipliers approach, the proposed method considers the calculation of the critical forcing amplitude as an optimization problem with constraints that are imposed by the existence of locations of vertical tangency. In comparison with the Gröbner basis method, the proposed approach is more straightforward and thus easy to apply for finding the critical forcing amplitude both analytically and numerically. Three examples are given to confirm the validity of the theoretical predictions. The first two present the analytical form for the critical forcing amplitude and the third one is an example of a numerically computed solution.

An Observation on Least Action Principle in Classical Mechanics Oriented on the Evaluation of Relativistic Error Concerning the Measurements of Light Propagating in a Liquid

2013 ◽  
pp. 166-176
Author(s):  
Alessandro Massaro ◽  
Piero Adriano Massaro
Keyword(s):  
Euler Equations ◽  
Classical Mechanics ◽  
First Integrals ◽  
Action Principle ◽  
Classical Approach ◽  
Limit Case ◽  
Least Action Principle ◽  
Calculus Of Variation ◽  
Least Action ◽  
Approximate First Integrals

The authors prove that the standard least action principle implies a more general form of the same principle by which they can state generalized motion equation including the classical Euler equation as a particular case. This form is based on an observation regarding the last action principle about the limit case in the classical approach using symmetry violations. Furthermore the well known first integrals of the classical Euler equations become only approximate first integrals. The authors also prove a generalization of the fundamental lemma of the calculus of variation and we consider the application in electromagnetism.

On Asymptotic Approximations of First Integrals for Weakly Nonlinear Oscillators

2001 ◽  
Author(s):  
S. B. Waluya ◽  
W. T. van Horssen
Keyword(s):  
Perturbation Method ◽  
Periodic Solutions ◽  
Nonlinear Oscillator ◽  
Nonlinear Oscillators ◽  
First Integrals ◽  
Asymptotic Approximations ◽  
Weakly Nonlinear ◽  
Time Periodic Solutions ◽  
Time Periodic

Abstract In this paper a nonlinear oscillator problem will be studied. It will be shown that the recently developed perturbation method based on integrating vectors can be used to approximate first in tegrals and periodic solutions. The existence, uniqueness, and stability of time-periodic solutions are obtained by using the approximations for the first integrals.

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