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Advanced Engineering Dynamics
R. Valéry Roy
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Front Matter
Colophon
Dedication
Preface
OVERVIEW OF THE BOOK
METHODOLOGY
HOW TO USE THIS BOOK
1
Position and Displacement
1.1
Parametrization of the Position a Rigid Body
1.2
Coordinate Systems
1.2.1
Cartesian Coordinate System
1.2.2
Cylindrical Coordinate System
1.2.3
Spherical Coordinate System
1.3
Orientation of a Rigid Body: Direction Cosines
1.4
Orientation of a Rigid Body: Euler Angles
1.5
Orientation of a Rigid Body: Equivalent Angle/Axis of Rotation
1.6
Orientation of a Rigid Body: Quaternions
1.7
Finite Displacement of a Rigid Body
1.7.1
Translation
1.7.2
Rotation
1.7.3
Screw Displacement
1.7.4
Displacements Under Small Angle Rotations
1.8
Problems
2
Particle Kinematics
2.1
Referentials
2.2
Velocity and Acceleration of a Particle
2.3
Calculation of Velocity and Acceleration
2.3.1
Cartesian Coordinates of Velocity and Acceleration
2.3.2
Cylindrical Coordinate System
2.3.3
Spherical Coordinate System
2.4
Kinematics in Normal/Tangential Components
3
Rigid Body Kinematics
3.1
Angular Velocity of a Rigid body
3.2
Practical Determination of Angular Velocity
3.3
Direction Cosines and Angular Velocity
3.4
Quaternions and Angular Velocity
3.5
Angular Acceleration
3.6
Velocity Field of a Rigid Body
3.7
Problems
4
Screw Theory
4.1
Definition
4.2
Basic Operations on Screws
4.3
Properties of Screws
4.4
Couples and Sliders
4.5
The Sum of two Sliders
4.6
The Axis of a Screw
4.7
Product of Two Screws
4.8
A Special Class of Screws
4.9
Time-derivative of Screws
4.10
Problems
5
Kinematic Screw of a Rigid Body
5.1
The Kinematic Screw
5.2
Fundamental Decomposition
5.3
Special Cases
5.4
Examples
5.5
Acceleration Field of a Rigid Body
5.6
Problems
6
Relative Motion Analysis
6.1
Transport Velocity and Acceleration
6.2
Relative Motion Analysis: Velocity
6.3
Relative Motion Analysis: Acceleration
6.4
Special Cases and Examples
6.4.1
Translation
6.4.2
Rotation
6.4.3
Examples
6.5
Kinematic Loop Formula
6.6
Kinematics: Summary
6.7
Problems
7
Kinematics of Constrained Bodies
7.1
Constraints Between Rigid Bodies
7.1.1
Geometric versus kinematic constraints
7.1.2
Examples of Geometric Constraints
7.2
Kinematic Pairs
7.2.1
Lower kinematic pairs
7.2.1.1
Slider
7.2.1.2
Pivot
7.2.1.3
Slider-Pivot
7.2.1.4
Helical Joint
7.2.1.5
Spherical Joint
7.2.1.6
Planar Joint
7.2.2
Higher kinematic pairs
7.2.3
Example: The circular slider
7.3
Point Contact between Two Rigid Bodies
7.3.1
Assumptions
7.3.2
The slip velocity of a rigid body
7.3.3
Pivoting and Rolling of a Rigid Body
7.3.4
The Axodes of a Rigid Body Motion
7.3.5
Examples
7.4
Planar Kinematics
7.4.1
Instantaneous center of rotation
7.4.2
The fixed and moving centrodes
7.4.3
Kennedy’s theorem
7.4.4
Instantaneous Center of Acceleration
7.5
Problems
8
Kinematic Analysis of Mechanisms
8.1
General Methodology
8.2
Geometric Closure
8.3
Graphical Methods
8.4
Kinematic Closure
8.5
Problems
9
Mass Distribution
9.1
Material Systems
9.2
The Kinetic Screw of Material System
9.3
The Dynamic Screw of a Material System
9.4
Kinetic Energy
9.5
The Inertia Operator of a Rigid Body
9.6
Angular Momentum of a Rigid Body
9.7
Kinetic Energy of a Rigid Body
9.8
Extensions to System of Rigid Bodies
9.9
Examples
9.10
Problems
10
Mechanical Actions
10.1
Classification of Mechanical Actions
10.1.1
Internal versus External Forces
10.1.2
External Actions
10.1.3
Action-at-a-distance Screw
10.1.4
Contact Action Screw
10.1.5
The External Action Screw
10.2
Gravitational Interactions
10.2.1
Newton’s Law of Gravitation
10.2.2
Gravitational Field
10.2.3
Gravitational Field of a Body with Spherical Symmetry
10.2.4
Weight of a Particle and Gravitational Acceleration
10.3
Contact Actions
10.3.1
Frictionless Contact between two Rigid Bodies
10.3.2
Coulomb Laws of Sliding Friction
10.3.3
Rolling and Spinning Friction
10.3.4
Rigid Bodies in Line or Surface Contact
10.4
Frictionless Joints
10.4.1
Frictionless Pivot
10.4.2
Frictionless Slider
10.4.3
Frictionless Slider-Pivot
10.4.4
Frictionless Helical Joint
10.4.5
Frictionless Spherical Joint
10.4.6
Planar Frictionless Joint
10.5
Contact Action of a Fluid on a Rigid Body
10.5.1
Case 1: Static Case
10.5.2
Case 2: Effect of Fluid of a Rigid Body in Motion
10.6
Problems
11
Newton-Euler Formalism
11.1
The Principle of Virtual Power
11.1.1
Preliminaries: System of Particles
11.1.2
Generalization to Arbitrary Material Systems
11.1.3
Corollary: action and reaction screws
11.2
Fundamental Theorem of Dynamics
11.2.1
Derivation
11.2.2
A Class of Newtonian Referentials
11.2.3
Approximate Newtonian Referentials
11.2.4
Examples
11.3
Conservation Laws: First Integrals of Motion
11.3.1
Conservation of Linear Momentum
11.3.2
Conservation of Angular Momentum
11.4
Special Motions
11.4.1
Rigid Body in Rotation about a Fixed Axis
11.4.2
Euler-Poinsot Motion
11.5
Dynamic Balancing
11.6
Solution of Multibody Problems
11.7
Quaternionic Formulation
11.8
Problems
12
Power, Work & Energy
12.1
Power, Work, and Kinetic Energy
12.2
Power of External Action
12.3
Power of Internal Actions
12.4
Potential Energy
12.4.1
Potential Energy Associated with External Actions
12.4.2
Potential Energy of Interaction
12.5
Ideal Joints
12.6
The Kinetic Energy Theorem
12.6.1
Case 1: Single Rigid Body
12.6.2
Case 2: System of Rigid Bodies
12.7
Examples
12.8
Problems
13
Lagrange Equations
13.1
Partial Kinematic Screws
13.2
Lagrange Kinematic Formula
13.3
Power Coefficients
13.4
Lagrange Equations: Single Body
13.5
Lagrange Equations: System of Rigid Bodies
13.6
Lagrange Equations with Multipliers
13.7
Painlevé Equation
13.8
Lagrange vs Newton-Euler Formalisms
13.9
Problems
14
Gibbs-Appell & Kane Equations
15
Gyroscopic Phenomena
15.1
Examples of Gyroscopic Phenomena
15.2
Gyroscope: Definition
15.3
Dynamic Characterization of Gyroscopes
15.4
Motion of a Gyroscope about a Fixed Point
15.5
The Gyroscopic Approximation
15.6
Applications
15.7
Problems
16
Non-Newtonian Referentials
Backmatter
A
Vector Algebra
A.1
Vector Algebra
A.1.1
Vectors
A.1.2
Scalar Product
A.1.3
Cross Product
A.1.4
Triple Scalar Product
A.1.5
Linear Operators
A.2
Problems
B
Table of Mass Moments of Inertia
B.1
Tables of Mass Moment of Inertia
B.1.1
One-dimensional bodies
B.1.2
Two-dimensional bodies
B.1.3
Three-dimensional bodies
C
List of Symbols
Index
Colophon
Colophon
Colophon
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