Fig. 6. Schematic diagram of coordinate systems employed in the model. The origin of the global, inertial coordinate system is located at the mean vertical position of the shoulder joint and travels forward at constant mean velocity (see also Fig. 2); its path is indicated by the horizontal dotted line, and its location at mid-upstroke is given in the center of the figure. The origin of the global, non-inertial coordinate system is located at the shoulder joint and accelerates vertically and horizontally with the bat. It is shown at three points in the wingbeat cycle: late downstroke (left), mid-upstroke (center) and late upstroke (right). For both these coordinate systems, the x axis is directed perpendicular to the plane of the page, directly to the bat's right. At mid-upstroke and mid-downstroke, the global inertial and non-inertial axes coincide (center). The true flight path of the shoulder is indicated by the dashed line. Local x, y, z coordinate systems can be centered at any anatomical point of interest, such as the shoulder, the midshaft of the humerus or radius or the carpus. In this illustration, the axes of a local (x, y, z) coordinate system with its origin at the humeral midshaft are shown by gray heavy dashed lines; once again, the x axis is directed perpendicular to the plane of the page. Local primed (x', y', z') coordinate systems are employed for computations of local stresses, etc; they are centered at the origin of a corresponding (x, y, z) coordinate system, but are rotated such that the x axis is directed along the length of the humerus (or radius) and the y axis is directed perpendicular to the local wing surface. The local (x', y', z') coordinate system at the humeral midshaft is illustrated here, with axes depicted by barred black lines. Late in the upstroke (rightmost illustration), from a lateral view as depicted here, the undersurface of the wing would be interposed between the observer and the x' and y' axes; this is depicted schematically by gray shading.