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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 89
PROCEEDINGS OF THE SIXTH INTERNATIONAL CONFERENCE ON ENGINEERING COMPUTATIONAL TECHNOLOGY
Edited by: M. Papadrakakis and B.H.V. Topping
Paper 161

Computational Biomechanics, Stochastic Motion and Team Sports

E. Grimpampi1, A. Pasculli2 and A. Sacripanti1,3

1School of Medicine and Surgery, University of Rome "Tor Vergata", Italy
2Faculty of Mathematics, Physics and Natural Sciences, University "G. D'Annunzio", Chieti-Pescara, Italy
3Advanced Physics Technology and New Materials (FIM), ENEA, Italy

Full Bibliographic Reference for this paper
E. Grimpampi, A. Pasculli, A. Sacripanti, "Computational Biomechanics, Stochastic Motion and Team Sports", in M. Papadrakakis, B.H.V. Topping, (Editors), "Proceedings of the Sixth International Conference on Engineering Computational Technology", Civil-Comp Press, Stirlingshire, UK, Paper 161, 2008. doi:10.4203/ccp.89.161
Keywords: sport biomechanics, stochastic modelling, Brownian motion, complex many-particle systems, dual sports, self organization.

Summary
This paper presents the extension of a general model for all the "situation sports" [1], both team and dual. A computational model of the motion of a single team player is presented, and the resulting trajectory is compared with the one obtained from experimental data using match analysis software during competitions. It is assumed that the player has many "interactions" due to tackles, strategy changing, adversary contact and so on. Between each interaction it is assumed that he follows a straight line and his motion is characterized by viscous, pushing and "pedestrian like" force. A random Langevin force [2] is assumed to influence only the trajectory direction after each interaction. Furthermore it is assumed that the time step between each interaction is a random variable belonging to a Gaussian distribution. Consequently an average direction along which the player moves is selected and other reasonable assumptions are made in order to build an "objective function". The main criteria is a selection of a function correlated to the strategy of the player, around which, in a necessarily randomly way, a tactic function should be added. The strategy depends on the players' role.

For the numerical simulations in this paper, a forward player was selected, having as a "typical" target to score. So it is straightforward to assume that the line direction joining the player position and a point related to the goal, would be the main "strategy objective function" around which a random angle thetarand, expression of the "tactic objective action", influencing the direction selected by the player until the next interaction can be introduced. The random variable thetarand is assumed to be given by a Gaussian distribution. To introduce an "equivalent force", due essentially to tactic player reasoning, it is assumed that at each point of the field a different variance sigmatheta(x,y), of the thetarand is associated. This means that a player tactic action, specific to the area in which he is located, is considered as a random perturbation, superimposed to the player strategic reasoning. Thus an average angle thetam(x,y), function also of the player position, could be interpreted as the strategic objective, while a variable term is the tactics action associated with each point.

The noteworthy outcome is that the motion of the centre of mass for the couple of athletes in fighting sports competition is very well modelled as a classical Brownian motion, while the motion in a team sports competition is modelled by a more general class of Brownian motions, such as the active Brownian motions [3].

References
1
A. Sacripanti, "Breve dissertazione su di un sistema fisico complesso", ENEA-RT-INN/24, 1997.
2
W.T. Coffey, Yu.P. Kalmykov, J.T. Waldron, "The Langevin Equation: With Applications to Stochastic Problems in Physics, Chemistry and Electrical Engineering", Second Edition, World Scientific, River Edge, NJ, 2004.
3
W. Ebeling, "Active Brownian motion of pairs and swarms of particles", Acta Physica Polonica B, 38 (5), 1657-1671, 2007.

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