Abstract
We completely classify the first integrals of scalar non-linear second-order ordinary differential equations (ODEs) in terms of their Lie point symmetries. This is performed by first obtaining the classifying relations between point symmetries and first integrals of scalar non-linear second-order equations which admit one, two and three point symmetries. We show that the maximum number of symmetries admitted by any first integral of a scalar second-order non-linear ODE is one which in turn provides reduction to quadratures of the underlying dynamical equation. We provide physical examples of the generalized Emden-Fowler, Lane-Emden and modified Emden equations.
Original language | English |
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Pages (from-to) | 52-59 |
Number of pages | 8 |
Journal | International Journal of Non-Linear Mechanics |
Volume | 59 |
DOIs | |
Publication status | Published - Jan 2014 |
Externally published | Yes |
Keywords
- Emden-Fowler
- First integrals
- Lane-Emden
- Modified Emden
- Non-linear ordinary differential equations
- Symmetry
ASJC Scopus subject areas
- Mechanics of Materials
- Mechanical Engineering
- Applied Mathematics