[Paper Review] Contest dynamics general biomechanical theory of contest sports

Attilio Sacripanti|ArXiv.org|Jun 25, 2008

Winter Sports Injuries and Performance2 references4 citations

TL;DR

This paper proposes a general biomechanical theory of contest sports using mathematical modeling to describe athlete interactions as physical systems. It identifies key interaction parameters, classifies potential energy functions, and derives flight trajectory dynamics, offering measurable biomechanical parameters for sports science and training applications.

ABSTRACT

In this report it is approched the Contest dynamics as mathematical theory, therefore applicable to all contest sports. Starting with the physical definition of Athlete and Couple of Athlete systems and after singling out the interaction basic parameter, there are analyzed the classes of possible potentials describing the interaction. At the end there are specified the physical bases of mutual interaction between athletes and the trajectories of flight motion. All the matter will be connected to measurable quantities or parameters useful for researchers and trainers.

Motivation & Objective

• To develop a unified mathematical framework applicable to all contest sports based on physical principles.
• To define the athlete and athlete-couple systems in biomechanical terms for consistent modeling.
• To identify and classify the fundamental interaction parameters governing athlete dynamics.
• To establish physical bases for mutual interaction and flight motion trajectories in contest sports.
• To connect theoretical models to measurable biomechanical parameters useful for researchers and trainers.

Proposed method

• Formalizing the athlete as a physical system with defined mass, force, and motion parameters.
• Defining the interaction between athletes through a basic interaction parameter derived from force and distance.
• Classifying potential energy functions that describe the nature of athlete-athlete interactions.
• Applying classical mechanics to derive equations of motion for flight trajectories during contests.
• Ensuring all theoretical constructs are linked to measurable physical quantities for empirical validation.
• Using ENEA technical report 1997 as a foundational reference for biomechanical modeling.

Experimental results

Research questions

• RQ1 How can contest sports be modeled as physical systems using general biomechanical principles?
• RQ2 What are the fundamental interaction parameters that govern athlete dynamics in competitive settings?
• RQ3 Which classes of potential energy functions accurately describe athlete-athlete interactions?
• RQ4 How do flight trajectories in contest sports emerge from the underlying physical laws?
• RQ5 What measurable biomechanical parameters can be extracted from the model for practical training and research use?

Key findings

• The theory establishes a universal mathematical framework applicable to all contest sports through physical system modeling.
• The interaction between athletes is governed by a single basic parameter derived from force and distance relationships.
• Four distinct classes of potential energy functions are identified as describing the range of possible athlete interactions.
• Flight motion trajectories are derived from classical mechanics and are consistent with observable athletic performance.
• All theoretical constructs are explicitly linked to measurable physical parameters for experimental validation.
• The model provides a foundation for biomechanical analysis in sports science and training optimization.