Page 12 - Dynamics of Mechanical Systems

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Contents

Chapter 1 Introduction................................................................................................................1
1.1 Approach to the Subject......................................................................................................1
1.2 Subject Matter.......................................................................................................................1
1.3 Fundamental Concepts and Assumptions.......................................................................2
1.4 Basic Terminology in Mechanical Systems......................................................................3
1.5 Vector Review .......................................................................................................................5
1.6 Reference Frames and Coordinate Systems.....................................................................6
1.7 Systems of Units...................................................................................................................9
1.8 Closure .................................................................................................................................11
References.......................................................................................................................................11
Problems .........................................................................................................................................12

Chapter 2 Review of Vector Algebra ......................................................................................15
2.1 Introduction.........................................................................................................................15
2.2 Equality of Vectors, Fixed and Free Vectors..................................................................15
2.3 Vector Addition ..................................................................................................................16
2.4 Vector Components............................................................................................................19
2.5 Angle Between Two Vectors.............................................................................................23
2.6 Vector Multiplication: Scalar Product.............................................................................23
2.7 Vector Multiplication: Vector Product ............................................................................28
2.8 Vector Multiplication: Triple Products............................................................................33
2.9 Use of the Index Summation Convention .....................................................................37
2.10 Review of Matrix Procedures...........................................................................................38
2.11 Reference Frames and Unit Vector Sets..........................................................................41
2.12 Closure .................................................................................................................................44
References.......................................................................................................................................44
Problems .........................................................................................................................................45

Chapter 3 Kinematics of a Particle..........................................................................................57
3.1 Introduction.........................................................................................................................57
3.2 Vector Differentiation ........................................................................................................57
3.3 Position, Velocity, and Acceleration ................................................................................59
3.4 Relative Velocity and Relative Acceleration..................................................................61
3.5 Differentiation of Rotating Unit Vectors ........................................................................63
3.6 Geometric Interpretation of Acceleration.......................................................................66
3.7 Motion on a Circle .............................................................................................................66
3.8 Motion in a Plane...............................................................................................................68
3.9 Closure .................................................................................................................................71
References.......................................................................................................................................71
Problems .........................................................................................................................................71
Chapter 4 Kinematics of a Rigid Body...................................................................................77
4.1 Introduction.........................................................................................................................77
4.2 Orientation of Rigid Bodies..............................................................................................77