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Fig. 1. Sketches of the reference frames and wing motion. (A) OXYZ is an inertial frame, with the XY plane in the stroke plane. oxyz is a frame fixed on the wing, with the x axis along the wing chord, and the y axis along the wing span. {phi} is the azimuthal angle of the wing, {alpha} is the angle of attack and R is the wing length. (B) The motion of a section of the wing.