  A strategy for finding transition paths connecting two stable basins is
presented. The starting point is the Hamilton principle of stationary action;
we show how it can be transformed into a minimum principle through the addition
of suitable constraints like energy conservation. Methods for improving the
quality of the paths are presented: for example, the Maupertuis principle can
be used for determining the transition time of the trajectory and for coming
closer to the desired dynamic path. A saddle point algorithm (conjugate
residual method) is shown to be efficient for reaching a ``true'' solution of
the original variational problem.
