Optimal evaluation of generalized Euler angles with applications to control

Given two linearly independent matrices in , and , every rotation matrix, , can be written as the product of alternate elements from the one-dimensional subgroups corresponding to and , namely . The parameters , are called Generalized Euler Angles. In this paper, the minimum number of factors required for the factorization of , as a function of , is evaluated. An algorithm is given to determine the generalized Euler angles, in the optimal factorization. The results can be applied to the bang–bang control, with minimum number of switches, of some classical and quantum systems. [Copyright &y& Elsevier]