Viscous flow of fluid film on outer surface of a sloped rotating cylinder in gravitational field is studied. Thickness of the fluid layer is assumed to be small compared to the cylinder radius, which allows asymptotic analysis. Governing equation for the thickness dynamics is derived. The equation accounts for viscous effects, gravity, centrifugal and capillary forces. A criterion for existence of steady flow on the sloped cylinder is obtained. Linear stability of stationary solution for the vertical cylinder is given. Film thickness response to oscillations of the cylinder axis around vertical line is studied. Numerical model is implemented for the case of arbitrary slope angle.

研究了重力场下倾斜旋转圆柱体外表面流体膜的粘性流动。假定流体层的厚度比圆柱半径小，可以进行渐近分析。得出了厚度动力学的控制方程。该公式考虑了粘性效应，重力，离心力和毛细作用力。获得了在倾斜圆柱体上存在稳定流的判据。给出了垂直圆柱体固定解的线性稳定性。研究了薄膜厚度对圆柱轴绕垂直线振荡的响应。对于任意倾斜角的情况，均采用数值模型。