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General mathematical concept of compensation in sports science with quantitative analysis in the case of sprinting performance
Author(s) -
Fuchs P. M.
Publication year - 1995
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670180605
Subject(s) - sprint , compensation (psychology) , mathematics , set (abstract data type) , function (biology) , kinematics , simple (philosophy) , mathematical statistics , calculus (dental) , mathematical economics , computer science , statistics , epistemology , psychology , medicine , philosophy , physics , software engineering , dentistry , classical mechanics , evolutionary biology , psychoanalysis , biology , programming language
In many of the known sports disciplines, especially in athletics, the criterion which determines the positions of the competitors is a simple physical value, mostly a time or a distance, and the athlete with the minimum or maximum, respectively, takes the first place. Moreover, sports science explains this criterion by a set of the so‐called basic abilities. Compensation means the balance of the inferiority of such a basic ability by the superiority of another one. In the following paper, a general abstract concept to analyse compensation in a quantitative way is presented first. It can be applied to any discipline with a measurable criterion, if, in addition, the performance can be described by a kinematic function. Second, the proceeding is worked out in detail for the short sprint based on the modelling of the velocity function of a sprinter and the indicators for his basic abilities in [6]. The two aspects of compensation, namely the set of indicators which belong to the same criterion and the improvement of the criterion caused by the improvement of a basic ability, are discussed in a quantitative way. They turn out to be describable by the mathematical structures of ‘surfaces of constant pure running time’ and certain gradients, respectively.