  Since their introduction, Lie group integrators have become a method of
choice in many application areas. Various formulations of these integrators
exist, and in this work we focus on Runge--Kutta--Munthe--Kaas methods. First,
we briefly introduce this class of integrators, considering some of the
practical aspects of their implementation, such as adaptive time stepping. We
then present some mathematical background that allows us to apply them to some
families of Lagrangian mechanical systems. We conclude with an application to a
nontrivial mechanical system: the N-fold 3D pendulum.
