The concept of 'optimal' path in classical mechanics

The significance of the concept of 'optimal' path in the framework of classical mechanics is discussed. The derivation of the local harmonic approximation and self-consistent collective coordinate method equations of the optimal path is based on a careful study of the concepts of local maximal decoupling and global maximal decoupling respectively. This exhibits the nature of the differences between these two theories and allows one to establish the conditions under which they become equivalent. (author)