Approximate solutions and numerical analysis of a spring-mass running model

• Autorzy: Wróblewska Zofia

Identyfikatory

DOI

10.14708/ma.v48i1.6507

Warianty tytułu

PL

Przybliżone rozwiązania i analiza numeryczna modelu masy sprężynowej dla biegania

• Języki publikacji: EN

Abstrakty

EN

The paper refers to the classic spring-mass model of running, which was created on the basis of an inverted elastic pendulum. A new approximate solution of the boundary value problem relayed to the governing system based on two nonlinear ordinary differential equations is introduced, which we get in this model in a natural way. We give theoretical support by deriving asymptotic behaviour of obtained approximations. Simulations show that new solutions turn out very well. Our results are illustrated with some practical examples.

PL

W pracy rozważamy klasyczny model masy sprężynowej dla biegania oparty na odwróconym elastycznym wahadle. Przedstawiamy nowe przybliżone rozwiązanie interesującego zagadnienia brzegowego dla układu dwóch nieliniowych równań różniczkowych, które w naturalny sposób uzyskujemy w tym modelu. Badamy asymptotyczne zachowanie uzyskanych aproksymacji i podajemy asymptotyczną postać współczynnika spężystości nogi dla małych kątów ataku. Symulacje pokazują, że nowe rozwiązanie wypadło bardzo dobrze i wykazało dużą zgodność przybliżenia z rozwiązaniem dokładnym. Nasze wyniki zostały zilustrowane kilkoma praktycznymi przykładami pokazując, że pomiary parametrów biegu lekkoatletów są bliskie wartościom uzyskanym z modelu.

Słowa kluczowe

EN

spring-mass model; running; elastic pendulum; boundary value problem; approximation solution; shooting method

PL

model masy sprężynowej; krok biegowy; wahadło sprężynowe; zagadnienie brzegowe; rozwiązanie przybliżone; metoda strzelania

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Mathematica Applicanda
• Rocznik: 2020
• Tom: Vol. 48, no. 1
• Strony: 25--48
• Opis fizyczny: Bibliogr. 33 poz., fot., rys., tab., wykr.

Twórcy

autor

Wróblewska Zofia

• Wrocław University of Science and Technology, Faculty of Pure and Applied Mathematics, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland

Bibliografia

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