Self-motion of an ellipsoid with controllable rotation in potential flow

• A prolate spheroidal complex as a single non-spherical body is adopted to investigate the self-motion of a body by the control of its own rotation through a potential flow without shed vortices. Based on the ‘sail effect’, the addedmass difference of the body in orientation is utilized to achieve various spatial self-motion patterns. • When the angular velocity of the body differs from the inner ball’s relative orbital angular velocity by 1/ n that of the ball, the body would take two types of closed trajectories of two periodic structures, epicycloids and hypocycloids, exhibiting closed movements of a long cycle in either anticlockwise or clockwise direction, which depends on the sign of difference between the two angular velocities, and all these closed trajectories contain 2n short-cycle symmetric loops inwards or outwards. • Two typical spatial self-motions along a specific direction without a retreat are identified. When the body’s rotational axis is set to pass through point o and not to coincide with its major axis, the body would persistently move forward, exhibiting a typical circular helix with chirality. When the body oscillates periodically about some minor axis, the inner ball moves along a closed curve just like a lemniscate, and 1 k, 2 k satisfy some condition, the body would also persistently move forward with a typical cylindrical helix pattern. The moving behaviors of a prolate spheroidal complex with the controllable rotation in an ideal fluid without vortex shedding are investigated to find out the self-propelled mechanism of a non-spherical swimmer via the self-controlled rotation coupled with shift of its internal mass. Based on the model, algebraic velocity vector equations for the complex are derived from the Kirchhoff equations. Several simple cases reveal that the single non-spherical body can push itself to move persistently forward to break the kinematic time-reversal symmetry through coupling the specially-appointed rotation with the corresponding cyclic shift of the internal mass, and some typical self-motion patterns such as trochoids in two dimensions and unidirectional spatial helical motions are identified. The study aims to provide a potential swimming manner of underwater vehicles.