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2022 | OriginalPaper | Chapter

Is Optimal Velocity Constant During Running?

Author : Ryszard Maroński

Published in: Biomechanics in Medicine, Sport and Biology

Publisher: Springer International Publishing

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Abstract

The minimum-time competitive run is reconsidered in the paper. The problem is formulated and solved in optimal control (calculus of variations). A non-classical method of Miele is applied – the method of extremization of line integrals by Green’s theorem. This method gives necessary and sufficient conditions of optimality. Two models of the energy conversions in competitor’s body are considered: the model of Keller and the model of Bonnans and Aftalion. It is shown that the optimal race may be broken into three phases: acceleration, cruise (along so-called singular arc), and final slowing down. The fundamental finding is that the optimal cruising velocity is constant for Keller’s model but it decreases for Bonnans and Aftalion’s model.

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previous chapter Assessing the Feasibility of Using Spherical Contact Pairs to Model the Contact Regions in the Joints of the Index Finger
next chapter Characteristics of Nerve Roots Mechanical Properties Exposed to Uniaxial Stretching Tests
Literature
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Keller, J.B.: A theory of competitive running. Phys. Today 26, 43–47 (1973)CrossRef
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Reardon, J.: Optimal pacing for running 400 m and 800 m track races. Am. J. Phys. 81, 428–435 (2013)CrossRef
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miele, a.: Extremization of linear integrals by Green’s theorem. In: Litmann G. (ed.) Optimization Techniques with Application to Aerospace System, pp. 69–98. Academic Press, New York (1962)
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Maroński, R.: On optimal velocity during cycling. J. Biomech. 27, 205–213 (1994)CrossRef
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Maroński, R., Samoraj, P.: Optimal velocity in the race over variable slope trace. Acta Bioeng. Biomech. 17, 149–153 (2015)
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maroński, r.: Strategie optymalne w mechanice lotu i biomechanice. Oficyna Wyd. Politechniki Warszawskiej 79–93 (2016) (in Polish)
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Maroński, R.: Minimum-time running and swimming: an optimal control approach. J. Biomech. 29, 245–249 (1996)CrossRef
11.
Aftalion, A., et al.: How to identify the physiological parameters and run the optimal race. Math. Action 7, 1–10 (2016)MathSciNetCrossRef
Metadata
Title
Is Optimal Velocity Constant During Running?
Author
Ryszard Maroński
Copyright Year
2022
Book
Biomechanics in Medicine, Sport and Biology

Print ISBN: 978-3-030-86296-1

Electronic ISBN: 978-3-030-86297-8

Copyright Year: 2022

DOI
https://doi.org/10.1007/978-3-030-86297-8_10