During aerospace operations, small high-speed axial piston pumps are subjected to severe shock and vibration, with time-variable base motions significantly affecting their performance. This paper presents a novel dynamic model for a small axial piston pump system subjected to time-variable base motions, with its accuracy further validated through modal testing. Based on the Lagrange principle, the dynamic equations of the five lumped mass points of the piston pump under base translational and rotational motions are formulated, taking into account the mounting positions within the aircraft structure. This study investigates various forms of base motion, including simple harmonic excitations and typical aircraft maneuvers. Specifically, the effects of pitching, yawing, and rolling motions during variable-speed level flight and rolling maneuvers are analyzed to evaluate their influences on natural frequencies and critical speeds. Additionally, the effects of different flight states on these dynamic characteristics are also examined in the absence of base disturbances. The findings offer valuable insights for the robust design and reliable operation of axial piston pumps in dynamic aerospace environments.