  This article presents the dynamic interpolation problem for locomotion
systems evolving on a trivial principal bundle $Q$. Given an ordered set of
points in $Q$, we wish to generate a trajectory which passes through these
points by synthesizing suitable controls. The global product structure of the
trivial bundle is used to obtain an induced Riemannian product metric on $Q$.
The squared $L^2-$norm of the covariant acceleration is considered as the cost
function, and its first order variations are taken for generating the
trajectories. The nonholonomic constraint is enforced through the local form of
the principal connection and the group symmetry is employed for reduction. The
explicit form of the Riemannian connection for the trivial bundle is employed
to arrive at the extremal of the cost function. The result is applied to
generate a trajectory for the generalized Purcell's swimmer - a low Reynolds
number microswimming mechanism.
