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PERIODIC SOLUTIONS OF STRONGLY QUADRATIC NON-LINEAR OSCILLATORS BY THE ELLIPTIC PERTURBATION METHOD

✍ Scribed by S.H. Chen; X.M. Yang; Y.K. Cheung

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
228 KB
Volume
212
Category
Article
ISSN
0022-460X

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✦ Synopsis

The elliptic perturbation method is applied to the study of the periodic solutions of strongly quadratic non-linear oscillators of the form x¨+ c1 x + c2 x 2 = ef(x, x˙), in which the Jacobian elliptic functions are employed. The generalized Van der Pol equation with f(x, x˙) = m0 + m1 x -m2 x 2 is studied in detail. Comparisons are made with the solutions obtained by using the Lindstedt-Poincare´method and Runge-Kutta method to show the efficiency of the present method.

πŸ“œ SIMILAR VOLUMES

PERIODIC SOLUTIONS OF STRONGLY QUADRATIC
PERIODIC SOLUTIONS OF STRONGLY QUADRATIC NON-LINEAR OSCILLATORS BY THE ELLIPTIC LINDSTEDT–POINCARΓ‰ METHOD
✍ S.H. CHEN; X.M. YANG; Y.K. CHEUNG πŸ“‚ Article πŸ“… 1999 πŸ› Elsevier Science 🌐 English βš– 144 KB

The elliptic Lindstedt}PoincareH method is used/employed to study the periodic solutions of quadratic strongly non-linear oscillators of the form xK #c x# c x" f (x,. xR ), in which the Jacobian elliptic functions are employed instead of the usual circular functions in the classical Lindstedt}Poinc

AN ELLIPTIC PERTURBATION METHOD FOR CERT
AN ELLIPTIC PERTURBATION METHOD FOR CERTAIN STRONGLY NON-LINEAR OSCILLATORS
✍ S.H Chen; Y.K Cheung πŸ“‚ Article πŸ“… 1996 πŸ› Elsevier Science 🌐 English βš– 411 KB

An elliptic perturbation method is presented for calculating periodic solutions of strongly non-linear oscillators of the form x¨+ c1x + c3x 3 = ef(x, x˙), in which the Jacobian elliptic functions are employed instead of usual circular functions in the conventional perturbation procedure. Three type

PERIODIC SOLUTIONS OF STRONGLY NON-LINEA
PERIODIC SOLUTIONS OF STRONGLY NON-LINEAR OSCILLATORS BY THE MULTIPLE SCALES METHOD
✍ F. LAKRAD; M. BELHAQ πŸ“‚ Article πŸ“… 2002 πŸ› Elsevier Science 🌐 English βš– 339 KB

The multiple scales method, developed for the systems with small non-linearities, is extended to the case of strongly non-linear self-excited systems. Two types of nonlinearities are considered: quadratic and cubic. The solutions are expressed in terms of Jacobian elliptic functions. Higher order ap

COMMENTS ON β€œA PERTURBATION-ITERATIVE ME
COMMENTS ON β€œA PERTURBATION-ITERATIVE METHOD FOR DETERMINING LIMIT CYCLES OF STRONGLY NON-LINEAR OSCILLATORS”
✍ Dai Decheng πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 125 KB

The new idea of calculation of limit cycles of strongly non-linear systems and its several numerical examples were presented in [1]. It is interesting to study the calculation of limit cycles of non-linear systems further, however some defects have been found in [1].

A perturbation-incremental method for th
A perturbation-incremental method for the calculation of semi-stable limit cycles of strongly non-linear oscillators
✍ Chen, S. H. ;Chan, J. K. H. ;Leung, A. Y. T. πŸ“‚ Article πŸ“… 2000 πŸ› John Wiley and Sons 🌐 English βš– 130 KB πŸ‘ 2 views

The semi-stable limit cycle and bifurcation of strongly non-linear oscillators of the form xK #g(x)" f (x, xR , )xR is studied by the perturbation-incremental method. Firstly, the ordinary di!erential equation is transformed into an integral equation by a non-linear time transformation, then the ini