Volume 3, Issue 6
Closed-Form Expression for the Exact Period of a Nonlinear Oscillator Typified by a Mass Attached to a Stretched Wire

Malik Mamode

Adv. Appl. Math. Mech., 3 (2011), pp. 689-701.

Published online: 2011-03

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  • Abstract

The exact analytical expression of the period of a conservative nonlinear oscillator with a non-polynomial potential, is obtained. Such an oscillatory system corresponds to the transverse vibration of a particle attached to the center of a stretched elastic wire. The result is given in terms of elliptic functions and validates the approximate formulae derived from various approximation procedures as the harmonic balance method and the rational harmonic balance method usually implemented for solving such a nonlinear problem.

  • Keywords

Nonlinear oscillator exact period elliptic integral

  • AMS Subject Headings

34A34 34C15 34C25

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COPYRIGHT: © Global Science Press

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@Article{AAMM-3-689, author = {Malik Mamode}, title = {Closed-Form Expression for the Exact Period of a Nonlinear Oscillator Typified by a Mass Attached to a Stretched Wire}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2011}, volume = {3}, number = {6}, pages = {689--701}, abstract = {

The exact analytical expression of the period of a conservative nonlinear oscillator with a non-polynomial potential, is obtained. Such an oscillatory system corresponds to the transverse vibration of a particle attached to the center of a stretched elastic wire. The result is given in terms of elliptic functions and validates the approximate formulae derived from various approximation procedures as the harmonic balance method and the rational harmonic balance method usually implemented for solving such a nonlinear problem.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.11-m1141}, url = {http://global-sci.org/intro/article_detail/aamm/190.html} }
TY - JOUR T1 - Closed-Form Expression for the Exact Period of a Nonlinear Oscillator Typified by a Mass Attached to a Stretched Wire AU - Malik Mamode JO - Advances in Applied Mathematics and Mechanics VL - 6 SP - 689 EP - 701 PY - 2011 DA - 2011/03 SN - 3 DO - http://doi.org/10.4208/aamm.11-m1141 UR - https://global-sci.org/intro/article_detail/aamm/190.html KW - Nonlinear oscillator KW - exact period KW - elliptic integral AB -

The exact analytical expression of the period of a conservative nonlinear oscillator with a non-polynomial potential, is obtained. Such an oscillatory system corresponds to the transverse vibration of a particle attached to the center of a stretched elastic wire. The result is given in terms of elliptic functions and validates the approximate formulae derived from various approximation procedures as the harmonic balance method and the rational harmonic balance method usually implemented for solving such a nonlinear problem.

Malik Mamode. (1970). Closed-Form Expression for the Exact Period of a Nonlinear Oscillator Typified by a Mass Attached to a Stretched Wire. Advances in Applied Mathematics and Mechanics. 3 (6). 689-701. doi:10.4208/aamm.11-m1141
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