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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The C. Neumann problem as a completely integrable system on an adjoint orbit


Author: Tudor Raţiu
Journal: Trans. Amer. Math. Soc. 264 (1981), 321-329
MSC: Primary 58F05; Secondary 70H05
MathSciNet review: 603766
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Abstract: It is shown by purely Lie algebraic methods that the $ {\text{C}}$. Neumann problem--the motion of a material point on a sphere under the influence of a quadratic potential--is a completely integrable system of Euler-Poisson equations on a minimal-dimensional orbit of a semidirect product of Lie algebras.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1981-0603766-3
PII: S 0002-9947(1981)0603766-3
Keywords: Complete integrability, adjoint orbit, Hamiltonian system, Euler-Poisson equations, Kirillov-Kostant-Souriau symplectic structure
Article copyright: © Copyright 1981 American Mathematical Society