Itroduction

Introduction

Many professional footballers are unknowingly teachers of nonlinear differential equations. That can be seen in the quality and curvature that many of them apply to make their free throws, that having been executed correctly wonders become a goal, for example; just remember that free kick from David Beckham England got classified to the quarterfinals of the last World Cup against Ecuador, the free kick scored in a playoff game of Euro 2004 against Greece or even the historic goal Roberto Carlos scored before the selection of France in a friendly in Lyon before the World 98 which many have said he has no explanation of why the ball takes the curvature.

Of course all these players did not develop their talent in an everyday place like a classroom. They learned their tricks for solving equations kicking a ball a few million times. So refined and experienced players changed the hours of theoretical physics by years of trial and error over the programmed. But what if these players had known all physical and equations behind the free throw, making a reality of this phenomenon that has amazed the world of football for many years and before.

The purpose of this thesis is to try and give an explanation of the operation and interaction of some physical laws established in the past, as the Magnus force, Reynolds numbers and Bernoulli's principle, of free kick soccer.

For those who are content with the ball travel in a straight line, there is also a benefit in understanding the physics behind those amazing shots, and makes us appreciate the amazing talent of these players. What they do borders on a miracle, optimizing three different forces, two of which are constantly changing when the ball is in flight.

The first force is the one we know best: gravity. It seems that there is much to discover about it, since remains constant. But despite all his influence in our lives, all their control over the entire cosmos and our ability to describe and mold their effects, do not understand the mechanisms of gravitational force. Of the four fundamental forces identified by physicists - strong nuclear, weak electric, electric static gravity and the gravitational force is the least understood. Today, physicists aim to reach the "Grand Unified Theory" where all these forces are joined in a physical model describing the overall behavior in the universe. At this point, the gravitational force is the problem, the force that resists the union.

Despite the mystery behind the mechanisms of gravity, physicists have been able to describe quite extensively the behavior of objects under the influence of gravity. Isaac Newton, English scientist and mathematician (among other things) on the 17th and 18th centuries, was the first person to propose a mathematical model describing the gravitational attraction between objects. Albert Einstein was based on this model in

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