  A new format for commutator-free Lie group methods is proposed based on
explicit classical Runge-Kutta schemes. In this format exponentials are reused
at every stage and the storage is required only for two quantities: the right
hand side of the differential equation evaluated at a given Runge-Kutta stage
and the function value updated at the same stage. The next stage of the scheme
is able to overwrite these values. The result is proven for a 3-stage third
order method and a conjecture for higher order methods is formulated. Five
numerical examples are provided in support of the conjecture. This new class of
structure-preserving integrators has a wide variety of applications for
numerically solving differential equations on manifolds.
