  In this article, we study control of electron-nuclear spin dynamics at
magnetic field strengths where the Larmor frequency of the nucleus is
comparable to the hyperfine coupling strength. The quantization axis for the
nuclear spin differs from the static B_0 field direction and depends on the
state of the electron spin. The quantization axis can be switched by flipping
the state of electron spin, allowing for universal control on nuclear spin
states. We show that by performing a sequence of flips (each followed by a
suitable delay), we can perform any desired rotation on the nuclear spins,
which can also be conditioned on the state of the electron spin. These
operations, combined with electron spin rotations can be used to synthesize any
unitary transformation on the coupled electron-nuclear spin system. We discuss
how these methods can be used for design of experiments for transfer of
polarization from the electron to the nuclear spins.
