Patrick Murphy, Trever Mellon, Claire McDaid, KieranMullany
The consept of a flat non-frictional billiard table in which the ball is allowed to rebound for a large number of iterations has been the subject of much study and is, in some sense, one of the more well known and well studied examples where one can see classical chaos. By classical we mean a system evolving through classical dynamics. The evolution of a dynamic system is governed by the equations of motion. The use of the term 'chaos theory' is somewhat controversial. When we say that motion of a system is chaotic it does not mean that the motion is random and unpredictable. It refers to a general approach and methodology when treating problems rather than to a coherent body of work that the work theory entails. The term chaos when applied to dynamical systems takes on a more rigorous meaning. It refers to the property that some dynamical systems possess with regard to the sensitivity of the response of the dynamics to tiny changes in the initial conditions. A chaotic system exhibits enormous changes in the dynamical evolution when only tiny changes are made to the initial conditions. The Butterfly Effect is often used as an example of this, which says that a butterfly flapping it's wings in China can effect the weather here in Ireland. Ridiculous? Well it certainly sounds so, but since the equations that govern the weather are also chaotic, tiny changes in the initial conditions for the weather can lead to large deviations, sometimes. A consequence of the enhanced sensitivity to minute variations in the initial conditions is that one must know the initial conditions to more accuracy in order to follow the evolving dynamics of a chaotic system.