The formulation of sloshing dynamics for a Dewar partially filled with cryogenic superfluid helium II driven by both gravity gradient and Jitter accelerations associated with spinning and/or slew motions in a microgravity environment is investigated. The jitter accelerations include slew motion, spinning motion, atmospheric drag on the spacecraft, spacecraft attitude motions arising from machinery vibrations, thruster firing, pointing control of spacecraft, and crew motion. The numerical computation of sloshing dynamics is carried out through the formulation of noninertial frame spacecraft-bound coordinates and the solution of three-dimensional formulations of time-dependent, partial differential equations subject to initial and boundary conditions. The examples given demonstrate how sloshing dynamics affects the liquid-vapor interface oscillations of cryogenic superfluid helium II driven by orbital accelerations of a spacecraft associated with spinning and/or slew motions.