Birds, fish and other animals routinely use unsteady
effects to save energy by alternating between phases
of active propulsion and passive coasting. Here,
we construct a minimal model for such behaviour
that can be couched as an optimal control problem
via an analogy to travelling with a rechargeable
battery. An analytical solution of the optimal control
problem proves that intermittent locomotion has
lower energy requirements relative to steady-state
strategies. Additional realistic hypotheses, such as
the assumption that metabolic cost at a given power
should be minimal (the fixed gear hypothesis),
a nonlinear dependence of the energy storage
rate on propulsion and/or a preferred average
speed, allow us to generalize the model and
demonstrate the flexibility of intermittent locomotion
with implications for biological and artificial systems.