We construct new separated coordinates for the Clebsch system on the arbitrary coadjoint orbit of E(3). We explicitly obtain the reconstruction formulae which are symmetric functions in the constructed separated variables and write the corresponding Abel-type equations. We show that the constructed separated variables generalize Neumann's separated variables from the special onto the general coadjoint orbit of E(3)
Skrypnyk, T. (2019). “Symmetric” separation of variables for the Clebsch system. JOURNAL OF GEOMETRY AND PHYSICS, 135, 204-218 [10.1016/j.geomphys.2018.09.014].
“Symmetric” separation of variables for the Clebsch system
Skrypnyk, T.
2019
Abstract
We construct new separated coordinates for the Clebsch system on the arbitrary coadjoint orbit of E(3). We explicitly obtain the reconstruction formulae which are symmetric functions in the constructed separated variables and write the corresponding Abel-type equations. We show that the constructed separated variables generalize Neumann's separated variables from the special onto the general coadjoint orbit of E(3)
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