The spin motion calculation using Lie method in collider nonlinear magnetic field

The Lie operator method of solving the spin motion equation in collider nonlinear fields is used. The matrix presentation of the spin Lie transformation for a particle passing through collider elements is obtained. The formulas for combined several spin turn transformations are calculated in vector, matrix, and operator forms for zero, first, and second powers components of dynamical variable vectors. The expressions for the frequency precession vector components in zero, first, and second powers on orbit motion and first powers on spin motion are obtained. The computer code algorithms for nonlinear spin motion calculation are discussed. >