# A MODEL FOR THE SIMULATION OF VISCERAL MASS DISPLACENT IN DROP JUMPING

### Abstract

INTRODUCTION - Drop jumps may be mathematically modelled as a mass spring. damper system with a sufficient accuracy (Aurin and Zatsiorsky, 1984). It was stated that a mass of internal viscera does not affect a maximum jumping height and a frequency of jumping. Minetti and Belli (1994) found visceral mass, which presents 14% of the total body mass, oscillating in an opposite phase than a musculosketal mass during hopping and thus significantly influencing the jumping height and frequency of jumping, but also an energy consumption as well. The aim of the visceral mass on jumping height in a single drop jump by mathematical modelling. The model (Fig. 1) consisted of two masses connected by a spring and damper, where mass M2 presented the visceral mass. Elastic module K2 and damping module 82 defined an attachment of M2 to the other parts of the body. The model was described with two differential equations: M , * I , - B 2 * x , + K , * x , - K , * X ? =O Adz * I 2 - B, *X, - KZ *x, =O where MI presented the mass of the external container, XaIn d x2 vertical displa-cements of M1 and M2 from a position of equilibrium, B2 the dam-ping coefficient, K1 and K2 the stiffness coefficients. Numerical solution was performed by MATLAB (The Math works Inc.) The vertical displacement of the centre of gravity of both masses (CG) was calculated by varying K2 and 82 systematically at constant K1. The value for K1 was taken from aurin and Zatsiorsky, 1984. The maximum jumping height was defined as the apex of the trajectory of CG. RESULTS - Dependence of jumping height on K2 and B2 is presented in fig.2. CONCLUSION - Greater K2 and B2 resulted in higher maximum jumping height, indicating the importance of a control of visceral mass for maximising the result. In practice, the greater K2 and 62 can be achieved by increased abdominal pressure. REFERENCES - Aurin, A.S., Zatsiorsky, V.M. (1984) Biomechanical characteristics of human ankle-joint muscles. Eur.J.Appl. Physiology 52: 400406. Minetti, A.E.,Belli, G. (1994) A model for the estimation of visceral mass displacement in periodic movements. J. Biomechanics 27: 97-1 01.
Section

Modelling / Simulation

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