中文摘要：

建立了4He量子干涉仪陀螺的数学模型，包括驱动方程，流量方程和位置方程。该数学模型可以完整地描述4He量子干涉仪陀螺系统。由驱动方程可知，采用热驱动的陀螺能够长期工作，但采用压力驱动的陀螺只能短时间工作。由流量方程可知，流过弱连接的超流体流量中，不仅含有表示旋转通量的交流流量，还含有由驱动引起的其他流量。位置方程表达了薄膜的位移，该位移是陀螺系统中唯一能被检测的物理量。基于实验参数的仿真验证了数学模型的有效性。根据本文建立的数学模型，可以进一步研究4He量子干涉仪陀螺的性能和分析该陀螺的误差。

英文摘要：

The mathematical model of 4He quantum interferometer gyroscope is presented. The model includes the driven equation, the current equation and the position equation. Therefore, it can sufficiently describe the gyro- scope system. The driven equation shows the thermally driven gyroscope can work for a long time but the pres- sure driven one cannot. From the current equation, the superfluid currents passing through the weak link contain the AC currents which show the rotation flux, and other currents caused by drive. As shown in the position equa- tion, the displacement of diaphragm is the only detectable parameter in the gyroscope system. The model is tested by the simulations based on experimental parameters, and can be used to research performance of the gyroscope and analyse the gyroscope error.