We solve a problem of separation of variables for the classical integrable hamiltonian systems possessing Lax matrices satisfying linear Poisson brackets with the non-skew-symmetric, non-dynamical elliptic so(3) â so(3) -valued classical r-matrix. Using the corresponding Lax matrices, we present a general form of the âseparating functionsâ B(u) and A(u) that generate the coordinates and the momenta of separation for the associated models. We consider several examples and perform the separation of variables for the classical anisotropic Eulerâs top, SteklovâLyapunov model of the motion of anisotropic rigid body in the liquid, two-spin generalized Gaudin model and âspinâ generalization of SteklovâLyapunov model.
Skrypnyk, T. (2017). Separation of variables in anisotropic models and non-skew-symmetric elliptic r-matrix. LETTERS IN MATHEMATICAL PHYSICS, 107(5), 793-819 [10.1007/s11005-016-0920-0].
Separation of variables in anisotropic models and non-skew-symmetric elliptic r-matrix
Skrypnyk, T
2017
Abstract
We solve a problem of separation of variables for the classical integrable hamiltonian systems possessing Lax matrices satisfying linear Poisson brackets with the non-skew-symmetric, non-dynamical elliptic so(3) â so(3) -valued classical r-matrix. Using the corresponding Lax matrices, we present a general form of the âseparating functionsâ B(u) and A(u) that generate the coordinates and the momenta of separation for the associated models. We consider several examples and perform the separation of variables for the classical anisotropic Eulerâs top, SteklovâLyapunov model of the motion of anisotropic rigid body in the liquid, two-spin generalized Gaudin model and âspinâ generalization of SteklovâLyapunov model.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.