Mathematical modelling and model-based simulation play an important role in sport and human movement science. Tactical analysis of team performance (e.g. in soccer), for example, requires sophisticated models for describing and covering the complexity of the underlying dynamic processes. Approaches from artificial intelligence and dynamical systems theory are widely applied. Optimization strategies in endurance sports such as running or cycling rely on models capable of simulating the relationship between load and performance. Models of various complexity of the neuro-muscular-skeletal system are applied in biomechanics and kinesiology in order to analyse or to simulate human motion, to explore skeletal muscle mechanics or to get more insight aspects of motor learning and control.
One particular challenge is the enormous amount of data (‘Big Data’) being captured during analysis in training and competition (e.g. by applying methods from computer vision).
This special issue is concerned with various approaches of modelling and analysing aspects of human movement in sport. Theoretical modelling approaches, but also practical results from different sports, are reported.
Four papers address methods for identifying patterns in two-dimensional positional data, which describe positions and movements of players in different game sports. Based on these patterns, models for describing and assessing player behaviour are developed.
Artificial neural networks are applied in order to analyse the interaction between teams in handball. Norbert Schrapf, Alsaied Shaimaa and Markus Tilp demonstrate that offensive and defensive playing patterns can be determined objectively. From this, the effectiveness of particular tactical actions can be assessed.
In the paper by Bartholomew Spencer, Sam Robertson and Stuart Morgan pairwise inter – and intra-team player movement coordination is assessed. As an example, data from Australian football are analysed. Relative phase properties are derived from angular velocity and acceleration data and applied to examine the degree of coupling among players.
Thomas Hoch, Xiaoying Tan, Roland Leser, Arnold Baca and Bernhard A. Moser present an explanatory computational model for the assessment of individual tactical skills in team sports on the example of soccer. Tactical behaviour of players rated from an expert’s perspective is modelled.
Recursive plots, which can be used for visualising the recurrence of states in a phase space, are applied by Michael Stöckl, Denise Plück, and Martin Lames. They demonstrate, how complex dynamic sport systems can thereby be analysed, and describe aspects of constructing such plots on the examples of soccer and golf.
The fifth paper gives an example from biomechanical modelling. Harald Penasso and Sigrid Thaller present a nonlinear parameter identification method for determining neuromuscular properties of individual knee-extensor muscles. They compare two mathematical models based on ordinary differential equations for simulating leg-extension experiments.
This special issue is based on selected contributions that were presented in a special session of the 8th MATHMOD conference in February 2015 in Vienna, Austria.