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Comparison of Different Approaches to Construct First Integrals for Ordinary Differential Equations
Joint Authors
Freire, Igor Leite
Naeem, Imran
Naz, R.
Source
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-15, 15 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-05-07
Country of Publication
Egypt
No. of Pages
15
Main Subjects
Abstract EN
Different approaches to construct first integrals for ordinary differential equations and systems of ordinary differential equations are studied here.
These approaches can be grouped into three categories: direct methods, Lagrangian or partial Lagrangian formulations, and characteristic (multipliers) approaches.
The direct method and symmetry conditions on the first integrals correspond to first category.
The Lagrangian and partial Lagrangian include three approaches: Noether’s theorem, the partial Noether approach, and the Noether approach for the equation and its adjoint as a system.
The characteristic method, the multiplier approaches, and the direct construction formula approach require the integrating factors or characteristics or multipliers.
The Hamiltonian version of Noether’s theorem is presented to derive first integrals.
We apply these different approaches to derive the first integrals of the harmonic oscillator equation.
We also study first integrals for some physical models.
The first integrals for nonlinear jerk equation and the free oscillations of a two-degree-of-freedom gyroscopic system with quadratic nonlinearities are derived.
Moreover, solutions via first integrals are also constructed.
American Psychological Association (APA)
Naz, R.& Freire, Igor Leite& Naeem, Imran. 2014. Comparison of Different Approaches to Construct First Integrals for Ordinary Differential Equations. Abstract and Applied Analysis،Vol. 2014, no. 2014, pp.1-15.
https://search.emarefa.net/detail/BIM-1015194
Modern Language Association (MLA)
Naz, R.…[et al.]. Comparison of Different Approaches to Construct First Integrals for Ordinary Differential Equations. Abstract and Applied Analysis No. 2014 (2014), pp.1-15.
https://search.emarefa.net/detail/BIM-1015194
American Medical Association (AMA)
Naz, R.& Freire, Igor Leite& Naeem, Imran. Comparison of Different Approaches to Construct First Integrals for Ordinary Differential Equations. Abstract and Applied Analysis. 2014. Vol. 2014, no. 2014, pp.1-15.
https://search.emarefa.net/detail/BIM-1015194
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1015194