One of methods to extract truncated Taylor map for orbital and spin motion in proton storage rings

The Taylor map coefficients obtained by any tracking code with differential algebra techniques accumulate two types of errors: computer rounding errors and errors defined by the size of integration step. There is an approach free from defects of the second type, the method of undetermined coefficients. Unfortunately it is not easy to produce a computer code for the usually used form of this method. In this paper we present algorithm combining the advantages of method of undetermined coefficients and the calculating elegance of Lie algebraic techniques. The general approach using only the common properties of Lie groups and Hamilton´s equations allows to obtain the truncated Taylor map for orbital and spin motion by the same way