2.6 Game 2302-0360 motion -- displacement and vectors

Table of contents

• Preface
  • General
  • Viewing tip
    • Figures
    • Listings
• General background information
• Discussion and sample code
  • Displacement
  • Addition and subtraction of vectors
  • Mathematical solutions
    • Using the Math.atan method
    • Mathematical solution to an earlier problem
    • Subtracting vectors
    • Adding more than two vectors
• Run the scripts
• Miscellaneous

Preface

General

This module is part of a series of modules designed for teaching the physics component of GAME2302 Mathematical Applications for Game Development at Austin Community College in Austin, TX. (See GAME 2302-0100: Introduction for the first module in the course along with a description of the course,course resources, homework assignments, etc.)

The purpose of this module is to introduce motion and to explain displacement and vector analysis.

Viewing tip

I recommend that you open another copy of this document in a separate browser window and use the following links to easily find and view the Figuresand Listings while you are reading about them.

Figures

• Figure 1 . A graphic showing displacement.
• Figure 2 . Vector diagram for a familiar example.
• Figure 3 . A triangle with sides of 30, 40, and ?.
• Figure 4 . Vector diagram for the sum of six vectors.
• Figure 5 . Illustration of the parallelogram law.
• Figure 6 . Screen output for Listing #1.
• Figure 7 . Screen output for Listing #2.
• Figure 8 . Screen output for Listing #3.

Listings

• Listing 1 . Using the Math.atan method.
• Listing 2 . The sum of two vectors.
• Listing 3 . The sum of four vectors.

General background information

Bodies - not a reference to people

To begin with, physics textbooks often refer to something called bodies . By this, they are not referring to living bodies or the carcasses of once livingcreatures. Instead, they are referring to what people might ordinarily call objects.

For example, somewhere in this series of modules, we will discuss something call ed a free body diagram . A free body diagram can be drawn relative to any object, such as a child sitting motionless in a swing on the playgroundor a piano hanging on a rope.

Rest and motion

While nothing in the universe is truly motionless (at rest), some things around us such as buildings seem to be at rest, while other things such asplanes, trains, and busses appear to be in motion.

There is no such thing as absolute rest. However, two bodies moving together at the same rate (with reference to some third body) may be deemed to be at restrelative to one another.

Therefore, if you are standing motionless on the Earth, you are at rest relative to the Earth with reference to the Sun.

Kinematics and kinetics

The fundamental properties of motion are often referred to as kinematics .

According to the course description, in addition to "applications of mathematics and science" , the course is also to include "the utilization of matrix and vector operations, kinematics, and Newtonianprinciples in games and simulations" ,

The relationships between motion and force are often referred to as kinetics . These are the topics that will be covered in this and the next several modules in this collection.