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First Integrals for Two Linearly Coupled Nonlinear Duffing Oscillators
Joint Authors
Naeem, I.
Naz, R.
Mahomed, Fazal Mahmood
Source
Mathematical Problems in Engineering
Issue
Vol. 2011, Issue 2011 (31 Dec. 2011), pp.1-14, 14 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2011-01-26
Country of Publication
Egypt
No. of Pages
14
Main Subjects
Abstract EN
We investigate Noether and partial Noether operators of point type corresponding to a Lagrangian and a partial Lagrangian for a system of two linearly coupled nonlinear Duffing oscillators.
Then, the first integrals with respect to Noether and partial Noether operators of point type are obtained explicitly by utilizing Noether and partial Noether theorems for the system under consideration.
Moreover, if the partial Euler-Lagrange equations are independent of derivatives, then the partial Noether operators become Noether point symmetry generators for such equations.
The difference arises in the gauge terms due to Lagrangians being different for respective approaches.
This study points to new ways of constructing first integrals for nonlinear equations without regard to a Lagrangian.
We have illustrated it here for nonlinear Duffing oscillators.
American Psychological Association (APA)
Naz, R.& Naeem, I.& Mahomed, Fazal Mahmood. 2011. First Integrals for Two Linearly Coupled Nonlinear Duffing Oscillators. Mathematical Problems in Engineering،Vol. 2011, no. 2011, pp.1-14.
https://search.emarefa.net/detail/BIM-501676
Modern Language Association (MLA)
Naz, R.…[et al.]. First Integrals for Two Linearly Coupled Nonlinear Duffing Oscillators. Mathematical Problems in Engineering No. 2011 (2011), pp.1-14.
https://search.emarefa.net/detail/BIM-501676
American Medical Association (AMA)
Naz, R.& Naeem, I.& Mahomed, Fazal Mahmood. First Integrals for Two Linearly Coupled Nonlinear Duffing Oscillators. Mathematical Problems in Engineering. 2011. Vol. 2011, no. 2011, pp.1-14.
https://search.emarefa.net/detail/BIM-501676
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-501676