  We analyze a class of high-amplitude, high-frequency oscillatory systems in
which periodicity occurs on two distinct time scales and establish the
convergence of its trajectories to a suitably averaged system by recursively
applying the averaging theorem. Moreover, we introduce a novel bio-inspired 3D
source seeking algorithm for rigid bodies with a collocated sensor and prove
its practical stability under typical assumptions on the source signal strength
field by combining our averaging results with singular perturbation.
