Fig. 1. Definition of kinematic frames of reference. The fixed lab frame (x_f, y_f, z_f) is a right-handed coordinate system with the positive z_f-axis pointing down towards the ground. A second frame of reference (x_b, y_b, z_b) has its origin at the fly's center of mass with the x_b-axis oriented along the long body axis towards the animal's head, the y_b-axis oriented parallel to the fly's right wing, and the z_b-axis positioned perpendicular to the x_b- and y_b-axes and directed towards the ventral surface of the animal. Right-wing down rotation about the x_b-axis is positive roll, nose-up rotation around the y_b-axis is positive pitch, and a turn to the fly's right around the z_b-axis is positive yaw. For each video frame, a unit quaternion q specifies the rotation from body-centered coordinates to the fixed lab coordinates necessary to achieve the attitude of the fly in that frame.