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This article presents the dynamic interpolation problem for locomotionsystems evolving on a trivial principal bundle $Q$. Given an ordered set ofpoints in $Q$, we wish to generate a trajectory which passes through thesepoints by synthesizing suitable controls. The global product structure of thetrivial 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 costfunction, and its first order variations are taken for generating thetrajectories. The nonholonomic constraint is enforced through the local form ofthe principal connection and the group symmetry is employed for reduction. Theexplicit form of the Riemannian connection for the trivial bundle is employedto arrive at the extremal of the cost function. The result is applied togenerate a trajectory for the generalized Purcell's swimmer - a low Reynoldsnumber microswimming mechanism.

Variational dynamic interpolation for kinematic systems on trivial principal bundles