A rotating elastic cylinder moving on an elliptic orbit

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.