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  • Electronic Resource  (4)
  • Mathematics and Statistics  (4)
  • 1
    Electronic Resource
    Electronic Resource
    General mathematical concept of compensation in sports science with quantitative analysis in the case of sprinting performance (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 473-505 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: 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.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670180605
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Physical model, theoretical aspects and applications of the flight of a ball in the atmosphere. Part III: Theory in the case of vertical angular frequency and in the general spin-case (1995)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 18 (1995), S. 201-223 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: If a ball is viewed as a rigid body, its flight in the atmosphere can be described by six ordinary differential equations, which has been derived in the first part of this paper.In this following third part, some further theoretical aspects in the case of vertical angular frequency will be pointed out using an unknown transformation of the original independent variable, i.e. the time, as indicated in Part II.Last, but not least, the general case of angular frequency is to be treated. A rough qualitative discussion of the solutions is given as well as - if the equations are viewed as a three-dimensional dynamical system - the unique stable equilibrium, which depends on the spin. This equilibrium turns out to be globally attractive, which can be proved by the construction of a suitable Ljapunov function. Then, the ball flight system can be transformed into a fourth-order scalar differential equation.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670180303
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Physical model, theoretical aspects and applications of the flight of a ball in the atmosphere. Part II: Theoretical aspects in the case of vertical angular frequency and applications (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991), S. 461-481 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: If a ball is viewed as a rigid body, its flight in the atmosphere can be described by a system of six ordinary differential equations, which has been derived in the first part of this paper.In this following second part, the theoretical aspects such as the curvature of the orbit and certain velocity functions will be investigated in the case of the vertical angular frequency of the rotating ball, in which the differential equations reduce to a planar dynamical system. This system turns out to be not explicity solvable.The solutions of the corresponding ordinary or boundary value problems. computed numerically, are used to treat certain problems in international ball games. for example, the maximum and minimum velocities of a volleyball service.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670140703
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Physical model, theoretical aspects and applications of the flight of a ball in the atmosphere. Part I: Modelling of forces and torque, and theoretical prospects (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991), S. 447-460 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A model of the forces and the torque operating on a ball that is flying with rotation in the atmosphere of the Earth, and the resulting system of ordinary differential equations, are derived from mechanics and aerodynamics.The system of equations allows the theoretical aspects of the flight of a ball, such as the boundedness of its kinetic energy, the curvature of the orbit or the velocity function, to be investigated using certain transformations of the variables.The solutions of the corresponding ordinary or boundary value problems, computed numerically, are used to treat certain tasks in international ball games, for example, the maximum and minimum velocities of a volleyball service.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670140702
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
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