  A method is presented to compute minimizers (instantons) of action
functionals using arclength parametrization of Hamilton's equations. This
method can be interpreted as a local variant of the geometric minimum action
method (gMAM) introduced to compute minimizers of the Freidlin-Wentzell action
functional that arises in the context of large deviation theory for stochastic
differential equations. The method is particularly well-suited to calculate
expectations dominated by noise-induced excursions from deterministically
stable fixpoints. Its simplicity and computational efficiency are illustrated
here using several examples: a finite-dimensional stochastic dynamical system
(an Ornstein-Uhlenbeck model) and two models based on stochastic partial
differential equations: the $\phi^4$-model and the stochastically driven
Burgers equation.
