Hamiltonian approach to nonlinear oscillators

A Hamiltonian approach to nonlinear oscillators is suggested. A conservative oscillator always admits a Hamiltonian invariant, H, which keeps unchanged during oscillation. This property is used to obtain approximate frequency–amplitude relationship of a nonlinear oscillator with acceptable accuracy. Two illustrating examples are given to elucidate the solution procedure.

[1]  J. R. Chang,et al.  Application of He's Energy Balance Method to a Nonlinear Oscillator with Discontinuity , 2009 .

[2]  Metin O. Kaya,et al.  Application of Modified He's Variational Method to Nonlinear Oscillators with Discontinuities , 2009 .

[3]  S. S. Ganji,et al.  Application of amplitude–frequency formulation to nonlinear oscillation system of the motion of a rigid rod rocking back , 2009 .

[4]  Zhao-ling Tao.  The frequency–amplitude relationship for some nonlinear oscillators with discontinuity by He's variational method , 2008 .

[5]  Zhong-Fu Ren,et al.  Application of He's amplitude–frequency formulation to nonlinear oscillators with discontinuities , 2009 .

[6]  Ji-Huan He,et al.  An Improved Amplitude-frequency Formulation for Nonlinear Oscillators , 2008 .

[7]  Ji-Huan He,et al.  Preliminary report on the energy balance for nonlinear oscillations , 2002 .

[8]  Ji-Huan He,et al.  Max-Min Approach to Nonlinear Oscillators , 2008 .

[9]  Ji-Huan He.  AN ELEMENTARY INTRODUCTION TO RECENTLY DEVELOPED ASYMPTOTIC METHODS AND NANOMECHANICS IN TEXTILE ENGINEERING , 2008 .

[10]  D. Ganji,et al.  He's Energy Balance Method for Nonlinear Oscillators with Discontinuities , 2009 .

[11]  Yiu-Yin Lee,et al.  Analysis of Strongly Nonlinear Oscillator using the Max-Min Approach , 2009 .

[12]  S. Gallego,et al.  A Novel Rational Harmonic Balance Approach for Periodic Solutions of Conservative Nonlinear Oscillators , 2009 .

[13]  Ji-Huan He.  Variational approach for nonlinear oscillators , 2007 .

[14]  Ahmet Yildirim,et al.  Determination of the frequency-amplitude relation for a Duffing-harmonic oscillator by the energy balance method , 2007, Comput. Math. Appl..

[15]  Davood Domiri Ganji,et al.  Application of the energy balance method to nonlinear vibrating equations , 2010 .

[16]  Ji-Huan He,et al.  A simple approach to nonlinear oscillators , 2009 .

[17]  Davood Domiri Ganji,et al.  Application of energy balance method and variational iteration method to an oscillation of a mass attached to a stretched elastic wire , 2010 .

[18]  M. Esmaeilpour,et al.  Solution of nonlinear cubic-quintic Duffing oscillators using He’s Energy Balance Method , 2009 .

[19]  Davood Domiri Ganji,et al.  Periodic Solution for Strongly Nonlinear Vibration Systems by He’s Energy Balance Method , 2009 .

[20]  De-Qiang Zeng,et al.  Nonlinear oscillator with discontinuity by the max–min approach , 2009 .

[21]  S. S. Ganji,et al.  HES ENERGY BALANCE AND HES VARIATIONAL METHODS FOR NONLINEAR OSCILLATIONS IN ENGINEERING , 2009 .

[22]  Dahua Shou,et al.  Variational approach to the nonlinear oscillator of a mass attached to a stretched wire , 2008 .