AAE 203 Class Notes - 1 AAE 203 Notes Martin Corless December 7 2009 2 Contents 1 Introduction 7 2 Units and Dimensions 9 2.1 Introduction 9 2.2

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Unformatted text preview: 1 AAE 203 Notes Martin Corless December 7, 2009 2 Contents 1 Introduction 7 2 Units and Dimensions 9 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.2 Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.2.1 SI system of units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.2.2 US system of units . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.2.3 Unit conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.3 Dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.3.1 Dimensional systems . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.4 Dimensions of derived quantities . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 3 Vectors 17 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 3.2 Vector addition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 3.2.1 Basic properties of vector addition . . . . . . . . . . . . . . . . . . . 24 3.2.2 Addition of several vectors . . . . . . . . . . . . . . . . . . . . . . . . 25 3.2.3 Subtraction of vectors . . . . . . . . . . . . . . . . . . . . . . . . . . 26 3.3 Multiplication of a vector by a scalar . . . . . . . . . . . . . . . . . . . . . . 26 3.3.1 Unit vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.4 Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 3.4.1 Planar case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 3.4.2 General case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.5 Products of Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 3.5.1 The angle between two vectors . . . . . . . . . . . . . . . . . . . . . . 42 3.5.2 The scalar (dot) product of two vectors . . . . . . . . . . . . . . . . . 43 3.5.3 Cross (vector) product of two vectors . . . . . . . . . . . . . . . . . . 47 3.5.4 Triple products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 4 Kinematics of Points 51 4.1 Derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 4.1.1 Scalar functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 4.1.2 Vector functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 4.1.3 The frame derivative of a vector function . . . . . . . . . . . . . . . . 54 3 4 CONTENTS 4.2 Basic definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 4.2.1 Position . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 4.2.2 Velocity and acceleration . . . . . . . . . . . . . . . . . . . . . . . . . 59 4.3 Rectilinear motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 4.4 Planar motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Planar motion ....
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This note was uploaded on 02/25/2010 for the course AAE 00203 taught by Professor ... during the Spring '10 term at Purdue University Calumet.

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AAE 203 Class Notes - 1 AAE 203 Notes Martin Corless December 7 2009 2 Contents 1 Introduction 7 2 Units and Dimensions 9 2.1 Introduction 9 2.2

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