A note on elliptic coordinates on the Lie algebra e(3)

Details A note on elliptic coordinates on the Lie algebra e(3) A note on elliptic coordinates on the Lie algebra e(3)

2006-09-08

arxiv.org/abs/nlin/0609019v2

Nonlinear Sciences

Exactly Solvable and Integrable Systems

4 pages, LaTeX and AmsTex. Accepted to J.Phys.A

Scientific paper

10.1088/0305-4470/39/38/L01

We introduce elliptic coordinates on the dual space to the Lie algebra e(3$
and discuss the separability of the Clebsch system in these variables. The
proposed Darboux coordinates on e^*(3) coincide with the usual elliptic
coordinates on the cotangent bundle of the two-dimensional sphere at the zero
value of the corresponding Casimir function.

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