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AN ELLIPTIC PERTURBATION METHOD FOR CERTAIN STRONGLY NON-LINEAR OSCILLATORS

✍ Scribed by S.H Chen; Y.K Cheung

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
411 KB
Volume
192
Category
Article
ISSN
0022-460X

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✦ Synopsis

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 types of Duffing-Van der Pol equation with f(x, x˙) = (1x 2 )x˙are studied in detail. The present method can give a second approximate solution and therefore its accuracy is much higher than that of other methods in which the solutions are only first approximations.

πŸ“œ SIMILAR VOLUMES

PERIODIC SOLUTIONS OF STRONGLY QUADRATIC
PERIODIC SOLUTIONS OF STRONGLY QUADRATIC NON-LINEAR OSCILLATORS BY THE ELLIPTIC PERTURBATION METHOD
✍ S.H. Chen; X.M. Yang; Y.K. Cheung πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 228 KB

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

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].

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