Matrix Methods Applied to Engineering Rigid Body Mechanics (eBook)

Front Cover 1
Matrix methods Applied to Engineering Rigid Body Mechanics 4
Copyright Page 5
Preface 6
Table of Contents 7
Principal Symbols and Notation 13
Chapter l. Kinematics 19
1.1 The Position Vector 19
1.2 The Relative Position Vector 20
1.3 Transformation of Vectors 21
1.4 The Rotation Matrix for Simple Rotations 26
1.5 Consecutive Rotations 28
1.6 Successive Transformation of Vectors 30
1.7 The Velocity and Acceleration of a Point 32
1.8 Small Rotations 36
1.9 Angular Velocity and the Derivative of the Rotation Matrix 38
1.10 The Relative Velocity of Points Fixed in a Rigid Body 41
1.11 The Central and Instantaneous Axes 44
1.12 The Relative Acceleration of Points Fixed in a Rigid Body 47
1.13 The Relative Acceleration of Coincident Points Which Have Relative Motion 51
1.14 Differentiation of the Angular Velocity Vector, a Special Case 52
1.15 Relative Angular Velocity 53
1.16 Relative Angular Acceleration 55
Chapter 2. Dynamics 56
2.1 Newton's Laws of Motion 56
2.2 The Measurement of Force 57
2.3 Work, Potential and Kinetic Energy 58
2.4 The Activity of a Force and its Relationship to the Rate of Change of Kinetic Energy 61
2.5 Impulse and Momentum 61
2.6 Centre of Mass 62
2.7 Force Moment, Moment of Momentum and Moment of Rate of Change of Momentum 63
2.8 The Linear Momentum of a Rigid Body 65
2.9 The Moment of Momentum of a Rigid Body Aboutits Centre of Mass 65
2.10 The Relationship Between Moments of Inertia Measured in Different Frames 68
2.11 The Rate of Change of Angular Momentum of a Rigid Body About its Centre of Mass 70
2.12 The Moment of Momentum of a Rigid Body About Any Point Q and the Rate of Change of Moment of Momentum About That Point 71
2.13 The Relationship Between the Moment of the External Forces and Couples on a Rigid Body About Any Point Q and the Rate of Change of Moment of Momentum About That Point 72
2.14 The Kinetic Energy of a Rigid Body 73
2.15 The Rate of Change of Kinetic Energy of a Rigid Body 74
2.16 The Special Case of the Motion of a Solid of Revolution 75
2.17 Rotation About a Fixed Axis 76
2.18 Principal Axes and Principal Moments of Inertia of a Rigid Body With a Plane of Symmetry 76
2.19 Principal Axes and Principal Moments of Inertia For Any Rigid Body 79
Chapter 3. Solution of Kinematics Problems 83
3.1 Solved Problems 83
3.2 Problems For Solution 159
Chapter 4. Solution of Dynamics Problems 182
4.1 Solved Problems 182
4.2 Problems For Solution 300
Answers to Problems For Solution Chapter 3 331
Answers to Problems For Solution Chapter 4 339
Bibliography 357