Fig. 3. Coordinate frames used to express kinematic data. (A) Translational positions and rotations were expressed in a coordinate (X,Y,Z) frame based on the mean direction of movement before perturbations and the global horizontal plane. (B) Translational velocities were expressed in a coordinate (x,y,z) frame based on the orientation of the fore—aft axis of the animals. (C—E) Rotation was expressed using yaw, pitch and roll Euler angles. Reaction forces from perturbations were directed towards the positive lateral axis.