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Integrable systems of quartic oscillators in ordinary (three-dimensional) space

S Iona and F Calogero

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A class of completely integrable, and indeed solvable, Hamiltonian many-body problems are exhibited, characterized by rotation-invariant Newtonian equations of motion (`acceleration equals force'), with linear and cubic forces, in ordinary (three-dimensional) space. The corresponding Hamiltonians are of normal type, with the kinetic energy quadratic in the canonical momenta and the potential energy quadratic and quartic in the canonical coordinates.


PACS

02.30.Ik Integrable systems

45.20.Jj Lagrangian and Hamiltonian mechanics

MSC

70E45 Higher-dimensional generalizations

70E40 Integrable cases of motion

70H08 Nearly integrable Hamiltonian systems, KAM theory

Subjects

Mathematical physics

Dates

Issue 13 (5 April 2002)

Received 15 January 2002, in final form 14 February 2002

Published 22 March 2002



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