3081 words - 13 pages

Group Simulation Model Analysis

Bouncing Ball Model: Use of Zero-Crossing Detection

2012

Executive Summary

In the system of a bouncing ball there are many factors which influence how the ball bounces. The 5 main components which affect how high the ball will bounce include the initial position of the ball, the initial velocity of the ball, the elasticity of the ball, the gravity of the selected area, and also the temperature of the material in which the ball was made from. These 5 major components of the basic system determine how high the ball bounces and how much energy was lost in the process of bouncing as well as allowing us to determine the relationship between ...view middle of the document...

This report aim is to identify the major components of this particular system and examine how changes one of these components will affect the way the ball bounces. This report also aims to explain some of the key variables involved when bouncing a ball, such as the elasticity of the material, the height dropped, the initial velocity of the ball, the gravity in which the ball is dropped, the mass of the ball, the hardness of the surface and also the temperature of the materials involved. All of these variables have a major impact on how the ball will bounce, as well as change the overall behaviour of the bouncing ball itself. This change will be determined through a sensitivity analysis of the most influential parameters of bouncing ball system such as the initial velocity and height. These will be further explained through the comparisons of various components and how they change depending on the other variables which helps to determine the relationships between the components in the system to see how they combine together to create a system which seems simple to a normal person, but in reality involves several components not visible in order to function as it does.

A bouncing ball model is a classic example of a hybrid dynamic system. A hybrid dynamic system is a system that involves both continuous dynamics, as well as, discrete transitions where the system dynamics can change and the state values can jump. This report aims to identify the major components and explain how changes the way the ball bounces will affect by the components, and to examine the key variables involved when bouncing a ball: the elasticity of the material, dropped by the height, the initial velocity, the gravity, the mass, the hardness of the surface and the temperature of the materials of the ball. These variables will affect on how the ball will bounce, and they can change the overall behaviour of the bouncing of the ball. The initial velocity and height are main of change will be determined through a sensitivity analysis of the most influential parameters of bouncing ball system. In this report will be further explained through the comparisons of various components and how they change depending on the other variables which help to determine the relationships between the components in the system.

References

1. Bernd Ulmann, Simulating a bouncing ball in a box,

http://www.vaxman.de/analog computing/bouncing ball bouncing ball.html

2. S. Ulam On some statistical properties of dynamical systems

J. Neyman, J.C. Oxtoby (Eds.), Proceedings of the fourth berkeley symposium on mathematical statistics and probability, vol. 3University of California Press, Berkeley (1961), pp. 315–320

2 System Overview and System Behaviour

The diagram below shows the factors that affect the bounce of a ball:

Figure1: Diagram of Variables affecting Bounce of the wall

Ball Material (Elasticity)

Elasticity is the ability inherent in most solid material that allows the...

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