Gibanje nogometne lopte pri slobodnom udarcu
| Autor: | Krnić, Josip |
|---|---|
| Přispěvatelé: | Bonačić Lošić, Željana, Cvitković, Mislav, Zoranić, Larisa |
| Jazyk: | chorvatština |
| Rok vydání: | 2023 |
| Předmět: | |
| Popis: | Među najzanimljivijim trenutcima u nogometnoj utakmici su slobodni udarci. Putanja lopte u letu pretežno ovisi o načinu na koji je lopta udarena. Posebno je fascinantna pojava zakretanja smjera gibanja lopte, koja je prouzročena Magnusovim efektom. Razumijevanje prirode sila koje se javljaju na loptu u letu je od praktične koristi za proizvođače nogometnih lopti i za same igrače. Motivacija ovog rada je opisati gibanje nogometne lopte pri slobodnom udarcu za proizvoljan udarac na loptu. Detaljno se obrađuju geometrija problema (koja uključuje modeliranje obrambenog zida) te različiti početni uvjeti i sile koje se javljaju na loptu u letu. Jednadžbe gibanja dane su drugim Newtonovim zakonom, uključuju sve relevantne sile na loptu, i rješavaju se numerički Runge-Kutta metodom 4. reda, uz zadane početne uvjete. Rješavanje jednadžbi gibanja daje traženu putanju lopte. Različite putanje prikazane su grafički na modelu nogometnog terena. Svi računi i grafički prikazi napravljeni su u Pythonu. Prikazano je i nekoliko teorijskih primjena modela. Dobiveni rezultati se vrlo dobro podudaraju s realnim očekivanjima. Free kicks are among the most interesting moments in a football match. The trajectory of a ball in the flight mostly depends on the way the ball is kicked. Especially fascinating is a phenomenon when the trajectory is being curved with respect to the initial direction of the shot, caused by the Magnus effect. Understanding the nature of the forces occuring on a ball in the flight is of a practical interest to both ball manufacturers and players. The goal of this thesis is to describe the motion of a soccer ball in a free kick, given an arbitrary impact on a ball. The geometry of the problem (including the modelling of a defensive wall) as well as different initial conditions and forces that act on a flying ball are elaborated in detail. The equations of motion are given by Newton's second law, comprise all the relevant forces on the ball and, given the initial conditions, are being solved numerically by the Runge-Kutta method of the 4th order. Solving the equations yields the desired trajectory of a ball. Different trajectories are shown graphically on a football field model. All the calculations and graphics are made in Python. A couple of different theoretical applications of the model are also shown. The final results match very well with the real-life expectations. |
| Databáze: | OpenAIRE |
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