We systematically investigate the ground state and dynamics of spinor Bose-Einstein condensates subject to a position-dependent detuning. This detuning induces three related quantities (a synthetic magnetic field, an angular velocity, and an angular momentum), which, due to trap anisotropy, may point in different directions. When the dipole frequencies along the three symmetric axes of the harmonic trap are degenerate, the dipole motion can decompose into two coupled transverse modes in the plane perpendicular to the synthetic magnetic field, and another decoupled longitudinal mode, enabling controllable Foucault-like precession or biconical trajectories depending on the excitation protocol. Furthermore, quenching the orientation of the synthetic magnetic field excites multiple coupled quadrupole modes. We develop a hydrodynamic theory whose predictions match well with Gross-Pitaevskii simulations. This study contributes to a deeper understanding of the effects of the synthetic magnetic field and the excitations of the collective mode in quantum fluids, providing a foundation for future developments in quantum simulation and high-precision sensing technologies.

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• Bose-Einstein condensates
• Collective effects in atomic physics
• Synthetic gauge fields