A single-rigid-body model for triple jump

A single-rigid-body model is used to approximately calculate total triple jump distance and phase ratios, given phase takeoff angles and last stride takeoff velocity. Each of the three phases contains two segments: support from touchdown to takeoff, and gravitational flight with air drag. Translational and rotational equations of motion including track reaction forces and moments describe center-of-mass translation and rotation during support segments. In each support, human muscular inputs shape the track reaction force. Two very simple assumptions are made about the orientation of the body during flight, namely that the body remains vertical and takes off with zero pitching angular momentum. Evaluation of the vertical and horizontal support impulses reveals takeoff angles as control variables and that the essential optimization problem can be viewed as choosing sequentially three takeoff angles to maximize total distance. To assess validity, numerical results are compared with actual competition measurements.