The Adiabatic Invariant of the Linear or Nonlinear Oscillator

1970 ◽  
Vol 11 (4) ◽  
pp. 1320-1330 ◽  
Author(s):  
K. R. Symon
Keyword(s):  
Nonlinear Oscillator ◽  
Adiabatic Invariant

Computation of the adiabatic invariant of the symmetric nonlinear oscillator $$d^2y \over dt^2+Q(\epsilon t)y^n=R(\epsilon t)y^m$$

1998 ◽  
Vol 9 (2) ◽  
pp. 187-194
Author(s):  
J. HU
Keyword(s):  
Nonlinear Oscillator ◽  
Nonlinear Oscillators ◽  
Adiabatic Invariant ◽  
Strongly Nonlinear ◽  
Strongly Nonlinear Oscillators

In a recent paper, the author showed that for certain symmetric bisuperlinear equations, cosine-like boundary behaviours will not yield symmetric solutions [1]. In this paper, we attack the adiabatic invariant problem by showing that, for these strongly nonlinear oscillators, the adiabatic invariant is intimately related to z′(0;∈) for a family of solutions.

Features of a chaotic attractor in a quasiperiodically driven nonlinear oscillator

2021 ◽  
Vol 31 (7) ◽  
pp. 073118
Author(s):  
V. P. Kruglov ◽  
D. A. Krylosova ◽  
I. R. Sataev ◽  
E. P. Seleznev ◽  
N. V. Stankevich
Keyword(s):  
Chaotic Attractor ◽  
Nonlinear Oscillator

Adiabatic invariant and evolution equations for the motion of a particle in a strongly inhomogeneous magnetic field

1982 ◽  
Vol 25 (9) ◽  
pp. 703-710
Author(s):  
K. Sh. Khodzhaev ◽  
A. G. Chirkov ◽  
S. D. Shatalov
Keyword(s):  
Magnetic Field ◽  
Evolution Equations ◽  
Inhomogeneous Magnetic Field ◽  
Adiabatic Invariant

Boosting the Output Performance of the Triboelectric Nanogenerator through the Nonlinear Oscillator

2021 ◽  
Vol 13 (5) ◽  
pp. 6331-6338
Author(s):  
Dong Guan ◽  
Guoqiang Xu ◽  
Xin Xia ◽  
Jiaqi Wang ◽  
Yunlong Zi
Keyword(s):  
Nonlinear Oscillator ◽  
Triboelectric Nanogenerator ◽  
Output Performance

scholarly journals Iterative reproducing kernel method for nonlinear oscillator with discontinuity

2010 ◽  
Vol 23 (10) ◽  
pp. 1301-1304 ◽  
Author(s):  
Boying Wu ◽  
Xiuying Li
Keyword(s):  
Nonlinear Oscillator ◽  
Reproducing Kernel ◽  
Kernel Method ◽  
Reproducing Kernel Method

scholarly journals Three-dimensional stochastic modeling of radiation belts in adiabatic invariant coordinates

2014 ◽  
Vol 119 (9) ◽  
pp. 7615-7635 ◽  
Author(s):  
Liheng Zheng ◽  
Anthony A. Chan ◽  
Jay M. Albert ◽  
Scot R. Elkington ◽  
Josef Koller ◽  
...  
Keyword(s):  
Stochastic Modeling ◽  
Three Dimensional ◽  
Radiation Belts ◽  
Adiabatic Invariant

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.

Sign in / Sign up

Export Citation Format

Share Document