Fig. 1.
The physics of tumbling. Jump elevation is determined by the beta angle (β), which is the angle between the horizontal and a line connecting the distal end of the tibia and the proximal end of the femur. The blue dot near the femur is the COM. The three beads along the dorsal thorax and the abdomen (numbered 1, 2 and 3) were used to measure pitch and abdominal flexion. Pitch (purple P) is the angle between the horizontal and a line segment through beads 1 and 2. Abdominal angle (θ) is the angle between a line through beads 1 and 2 and one through beads 2 and 3. Abdominal flexion is the difference in abdominal angle 6 ms after the feet leave the ground and the angle before they do so (θflex=θb–θa). (A) When the beta angle is large and the initial pitch is small, the COM is below the thrust vector. This causes a negative torque and negative pitch velocities (clockwise arrow). (B) If the beta angle is small and the pitch is large, the COM is above the thrust vector. This causes positive torques and positive pitch velocities (counter-clockwise arrow). (C) The COM is below the thrust vector so a negative torque is generated that promotes a head-downward rotation (green arrow). Activation of the dorsal longitudinal muscle creates a counter-torque that promotes a head-upward rotation (blue arrow) that offsets the torque from thrust. (D) When the feet leave the ground, the thrust and the torque generated from it both end. The counter-torque from the abdominal muscle is unopposed and causes a visible flexion of the abdomen.