The deformation of a rotating elastic cylinder moving on an elliptic orbit is discussed analytically. Firstly, one solution method is developed for a coupled displacement equation, which includes the centrifugal force and the 2D-Coriolis effects fully. Secondly, the obtained general solution is applied to a rotating cylinder moving on an elliptic orbit. For a rotating hollow cylinder, the non-circular deformation of its outer surface and the centrifugal/centripetal force produced by the motion on the elliptic orbit are discussed. It is shown that the non-circular deformation is more affected by the rotational velocity of the cylinder than by the angular velocity on the elliptic orbit. For a solid cylinder, the movement/displacement of the cylinder center is discussed, and some interesting and beautiful motion trajectory patterns are found. Due to the low-frequency nature in the practical applications, the low-frequency approximation is also carried out for all quantities, and it is confirmed that their approximate formulas are valid in the practical frequency range.

中文翻译：

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在椭圆轨道上运动的旋转弹性圆柱体

解析地讨论了在椭圆轨道上运动的旋转弹性圆柱体的变形。首先，开发了一种耦合位移方程的求解方法，该方程充分包含了离心力和二维科里奥利效应。其次，将得到的通解应用于在椭圆轨道上运动的旋转圆柱体。对于一个旋转的空心圆柱体，讨论了其外表面的非圆形变形和在椭圆轨道上运动产生的离心力/向心力。结果表明，与椭圆轨道上的角速度相比，非圆形变形受圆柱旋转速度的影响更大。对于实心圆柱体，讨论了圆柱体中心的运动/位移，并发现了一些有趣而漂亮的运动轨迹模式。