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Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA


Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania


On a Family of Integrable Hamiltonian Systems

Discontinuity, Nonlinearity, and Complexity 11(4) (2022) 751--755 | DOI:10.5890/DNC.2022.12.012

Nicola Sottocornola

Dept. of Mathematics and Statistics, Zayed University, Abu Dhabi, UAE

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We consider a family of Hamiltonian systems with homogeneous potentials $V_n$ of degree $n$. These systems are known to be Liouville integrable and their first integrals of motion are known. We examine first the easiest case where the potential function is a cubic polynomial and we find the separation coordinates. After we prove that all the systems in the family can be completely solved in quadratures using these new coordinates.


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