Physics – Mathematical Physics
Scientific paper
2009-02-02
Physics
Mathematical Physics
13 Pages, Contribution to the 4th Workshop on Group Analysis of Differential Equations and Integrable Systems, Protaras, Cypru
Scientific paper
In the three dimensional flat space any classical Hamiltonian, which has five functionally independent integrals of motion, including the Hamiltonian, is characterized as superintegrable. Kalnins, Kress and Miller have proved that, in the case of non degenerate potentials, i.e potentials depending linearly on four parameters, with quadratic symmetries, posses a sixth quadratic integral, which is linearly independent of the other integrals. The existence of this sixth integral imply that the integrals of motion form a ternary parafermionic-like quadratic Poisson algebra with five generators. The Kepler Coulomb potential that was introduced by Verrier and Evans is a special case of superintegrable system, having two independent integrals of motion of fourth order among the remaining quadratic ones. The corresponding Poisson algebra of integrals is a quadratic one, having the same special form, characteristic to the non degenerate case of systems with quadratic integrals.
Daskaloyannis Costas
Tanoudis Yannis
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