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Symmetries and Singularity Structures pp 65–77Cite as

Generalised Lie Symmetries and Integrability of Coupled Nonlinear Oscillators with Two Degrees of Freedom

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Abstract

We consider the integrability property of coupled polynomial nonlinear oscillators from the point of view of symmetries, with two degrees of freedom as a prototype example. It is shown how invariance of the equations of motion under generalised Lie transformations can lead to the identification of integrable cases. The perturbed Kepler problem is treated explicitly. Results on other two-dimensional systems are presented briefly.

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References

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Author information

Authors and Affiliations

  1. Department of Physics, Bharathidasan University, Tiruchirapalli, 620024, India

    M. Senthilvelan & M. Lakshmanan

Authors
  1. M. Senthilvelan
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  2. M. Lakshmanan
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Editor information

Editors and Affiliations

  1. Department of Physics, Bharathidasan University, Palkalaiperur Campus, 620 024, Tiruchirapalli, Tamilnadu, India

    Muthuswamy Lakshmanan  & Muthiah Daniel  & 

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© 1990 Springer-Verlag Berlin Heidelberg

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Senthilvelan, M., Lakshmanan, M. (1990). Generalised Lie Symmetries and Integrability of Coupled Nonlinear Oscillators with Two Degrees of Freedom. In: Lakshmanan, M., Daniel, M. (eds) Symmetries and Singularity Structures. Research Reports in Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-76046-4_7

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  • DOI: https://doi.org/10.1007/978-3-642-76046-4_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-53092-3

  • Online ISBN: 978-3-642-76046-4

  • eBook Packages: Springer Book Archive

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