MATHEMATICAL MODELS IN SPORT BIOMECHANICS

Abstract

Since the age of the ancient Creeks, for a very long time, the development of the athletic exercises have been based on the instinct or each single athlete and on his capability to evolve the technique by practicing. The improvement could be achieved only by means of long-suffering attempts based on previous results, empirically evaluated (and on the personal experiences of the trainer).In the modern age, from the institution of the modern Olympic games. a strong evolution process . has begun and still proceeds with a tremendous acceleration in order to overcame the limits of the best human performance continuously and almost in every sport. In the last few decades a big effort has been especially devoted to study the physiology applied the training techniques and the mechanical laws which regulate the. human body dynamic. The evolution of the high Jump technique Is an evident example of easily achievable results: the dorsal approach has been definitely adopted when It was clear that It minimize the elevation of the body center of mass and consequently of the required mechanical energy. However, this is a modest contribution of mechanics to sport. The recent evolution of computer and measuring systems (optoelectronic, elettrogonlometrlc etc. 1. that are now quite affordable. produced a great Impulse to the development of the mathematical models for the analysis and simulation of human body motion. Beside the kinematic analysis. two major dynamic questions are presently studied: the so called: "direct" and the "Inverse dynamic problems". Many researches face up to the second one. starting from the automatic analysis of the athlete motion, to compute the forces playing a role In the exercise (Inertla1 forces and couples, Joint forces and couples.etc.). On the other hand, so far, few works deal with the direct dynamic problem that substantially concerns the calculus of the body motion starting from the knowledge of the applied external forces. The solution of this problem allows the development of computer simulation packages that can be very profitable in sport coaching. As an example few programs can predict trajectory and orientation of the whole body during a flying phase of an hypothetical exercise, accepting as only Input the relative motion between the body segments (obviously the initial condition. the body geometry and the inertial parameters must also be known). Therefore these programs allow to plan and test exercises taking into account individual anthropometric characteristics; this 1s particularly interesting for dangerous exercises that can be preliminary checked without risk for the athlete.