  We consider a voltage-biased nanoelectromechanical Josephson junction, where
a suspended nanowire forms a superconducting weak-link, in an inhomogeneous
magnetic field. We show that a nonlinear coupling between the Josephson current
and the magnetic field generates a Laplace force that induces a whirling motion
of the nanowire. By performing an analytical and a numerical analysis, we
demonstrate that at resonance, the amplitude-phase dynamics of the whirling
movement present different regimes depending on the degree of inhomogeneity of
the magnetic field: time independent, periodic and chaotic. Transitions between
these regimes are also discussed.
