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Fig. 1. Sketches of the reference frames and wing motion. (A) oxyz is an inertial frame, with the xz plane in the stroke plane. o'x'y'z' is a frame fixed on the wing, with the x' axis along the wing chord and the z' axis along the wing span. {psi} is the azimuthal angle of the wing, {alpha} is the angle of attack and l is the distance between the y axis and the wing tip or the wing length. (B) The motion of a section of the wing.