An invariant classification of cubic integrals of motion

Details An invariant classification of cubic integrals of motion An invariant classification of cubic integrals of motion

2003-05-25

arxiv.org/abs/nlin/0305048v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

Scientific paper

We employ an isometry group invariants approach to study Killing tensors of valence three defined in the Euclidean plane. The corresponding invariants are found to be homogeneous polynomials of the parameters of the vector space of the Killing tensors. The invariants are used to classify the non-trivial first integrals of motion which are cubic in the momenta of Hamiltonian systems defined in the Euclidean plane. The integrable cases isolated by Holt and Fokas-Lagerstrom are investigated from this viewpoint.

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