High Jump Direct Dynanic Simulation

  • Bruno Zappa
  • Federico Casolo
  • Arrigo Vallata
Keywords: high jump

Abstract

High jumps are composed of a complex sequence of movements whose single contribution to the whole body motion cannot be intuitively predicted. While most of the movements are well calibrated by the elite athlete in order to reach the result, few other are not effective or negative by the mechanical point of view and are probably performed for an erroneous feeling of their effects. The direct dynamic simulation of jumping can be useful in order to deepen the mechanics of high jump techniques, to explain to the athletes the consequences of some errors and to test some possible evolution of the exercise. When the external forces and the relative movements of limbs are known, the calculation of the whole trajectory and orientation, is a direct dynamic problem. A mathematical method recently developed by our group in cooperation with the University of Brescia (Casolo, Legnani, 1990) has been used to build the software package for the direct dynamic simulation. The body model consists of 14 (or 16) rigid bodies mutually connected by means of a sequence of revolute pairs; the anthropometry and the mass distribution are calculated for each subject by means of regression equations based on the experimental data published by Ciauser et al. (1980). Input data for the simulation of the aerial phase of the high jump are: initial position, velocity and angular velocity of the whole body and the laws of motion (0 - f(t» of all the joints involved in the exercise. In order to understand and to optimize the exercise, we built the joints' l.o.m. starting from data collected during international meetings. If the initial generalized velocities matrix of the trunk (containing the three components of the angular velocity and the linear velocity of a point on the body at t=O) is calculated only a few frames after take-off, it is affected by the unavoidable errors of the experimental data reconstruction. Therefore, becuase the vertical component of the momentum during the aerial phase can easily be computed, while all other terms of the momentum matrix (which contains both the components of the momentum and of the angular momentum) remain constant, we correct the initial (t=O) momentum matrix by knowing the matrices along the flying phase. The joints l.o.m. are smoothed by quintic splines because they also are affected by errors in manual digitization. The check of the adequacy of the model and of the method is obtained by the direct dynamic simulation of the winning jump of the 1992 Olympic Games. Figure 1