دانلود کتاب Intermediate dynamics for engineers: Newton-Euler and Lagrandian mechanics

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Contents Preface Part I A Single Particle 1 Kinematics of a Particle 1.1 Introduction 1.2 Reference Frames 1.3 Kinematics of a Particle 1.4 Cartesian, Cylindrical Polar, and Spherical Polar Coordinate Systems 1.5 Curvilinear Coordinates 1.6 Examples of Curvilinear Coordinate Systems 1.7 Representations of Particle Kinematics 1.8 Kinetic Energy and Coordinate Singularities 1.9 Constraints 1.10 Classification of Constraints 1.11 Closing Comments 1.12 Exercises 2 Kinetics of a Particle 2.1 Introduction 2.2 The Balance Law for a Single Particle 2.3 Work and Power 2.4 Conservative Forces 2.5 Examples of Conservative Forces 2.6 Constraint Forces 2.7 Conservations 2.8 Dynamics of a Particle in a Gravitational Field 2.9 Dynamics of a Particle on a Spinning Cone 2.10 A Shocking Constraint 2.11 A Simple Model for a Roller Coaster 2.12 Closing Comments 2.13 Exercises 3 Lagrange’s Equations of Motion for a Single Particle 3.1 Introduction 3.2 Lagrange’s Equations of Motion 3.3 Equations of Motion for an Unconstrained Particle 3.4 Lagrange’s Equations in the Presence of Constraints 3.5 A Particle in Motion on a Smooth Surface of Revolution 3.6 A Particle in Motion on a Sphere 3.7 Some Elements of Geometry and Particle Kinematics 3.8 The Geometry of Lagrange’s Equations of Motion 3.9 Lagrange’s Equations of Motion for a Particle in the Presence of Friction 3.10 A Particle in Motion on a Helix 3.11 A Particle in Motion on a Moving Curve 3.12 Closing Comments 3.13 Exercises Part II A System of Particles 4 Lagrange’s Equations of Motion for a System of Particles 4.1 Introduction 4.2 A System of N Particles 4.3 Coordinates 4.4 Constraints and Constraint Forces 4.5 Conservative Forces and Potential Energies 4.6 Lagrange’s Equations of Motion 4.7 Construction and Use of a Single Representative Particle 4.8 Kinetic Energy, Mass Matrix, and Coordinate Singularities 4.9 The Lagrangian 4.10 A Constrained System of Particles 4.11 A Canonical Form of Lagrange’s Equations 4.12 Alternative Principles of Mechanics 4.12.1 Principle of Virtual Work and D’Alembert’s Principle 4.12.2 Gauss’ Principle of Least Constraint 4.12.3 Hamilton’s Principle 4.13 Closing Comments 4.14 Exercises 5 Dynamics of Systems of Particles 5.1 Introduction 5.2 Harmonic Oscillators 5.3 A Dumbbell Satellite 5.4 A Pendulum and a Cart 5.5 Two Particles Tethered by an Inextensible String 5.6 Closing Comments 5.7 Exercises Part III A Single Rigid Body 6 Rotations and their Representations 6.1 Introduction 6.2 The Simplest Rotation 6.3 Proper Orthogonal Tensors 6.4 Derivatives of a Proper Orthogonal Tensor 6.5 Euler’s Representation of a Rotation Tensor 6.6 Euler’s Theorem: Rotation Tensors and Proper Orthogonal Tensors 6.7 Relative Angular Velocity Vectors 6.8 Euler Angles 6.8.1 3–2–1 Euler Angles 6.8.2 3–1–3 Euler Angles 6.8.3 The Other Sets of Euler Angles 6.8.4 Application to Joint Coordinate Systems 6.8.5 Comments on Products of Rotations 6.9 Further Representations of a Rotation Tensor 6.10 Rotations, Quotient Spaces, and Projective Spaces 6.11 Derivatives of Scalar Functions of Rotation Tensors 6.12 Exercises 7 Kinematics of Rigid Bodies 7.1 Introduction 7.2 The Motion of a Rigid Body 7.3 The Angular Velocity and Angular Acceleration Vectors 7.4 A Corotational Basis 7.5 Three Distinct Axes of Rotation 7.6 The Center of Mass and Linear Momentum 7.7 Angular Momenta 7.8 Euler Tensors and Inertia Tensors 7.9 Angular Momentum and an Inertia Tensor 7.10 Kinetic Energy 7.11 Attitudes of Constant Angular Velocities 7.12 Closing Comments 7.13 Exercises 8 Constraints on and Potential Energies for a Rigid Body 8.1 Introduction 8.2 Forces and Moments Acting on a Rigid Body 8.3 Examples of Constrained Rigid Bodies 8.4 Constraints and Lagrange’s Prescription 8.5 Integrability Criteria 8.6 Potential Energies, Conservative Forces, and Conservative Moments 8.7 Closing Comments 8.8 Exercises 9 Kinetics of a Rigid Body 9.1 Introduction 9.2 Balance Laws for a Rigid Body 9.3 Work and Energy Conservation 9.4 Additional Forms of the Balance of Angular Momentum 9.5 Moment-Free Motion of a Rigid Body 9.6 The Baseball and the Football 9.7 Motion of a Rigid Body with a Fixed Point 9.8 Motions of Rolling Spheres and Sliding Spheres 9.9 Chaplygin’s Sphere 9.10 Closing Comments 9.11 Exercises 10 Lagrange’s Equations of Motion for a Single Rigid Body 10.1 Introduction 10.2 The Lagrange Top 10.3 Configuration Manifold of an Unconstrained Rigid Body 10.4 Lagrange’s Equations of Motion: A First Form 10.4.1 Proof of Lagrange’s Equations 10.4.2 The Four Identities 10.5 A Satellite Problem 10.6 Lagrange’s Equations of Motion: A Second Form 10.6.1 Summary 10.7 Lagrange’s Equations of Motion: Approach II 10.8 Rolling Disks and Sliding Disks 10.9 Lagrange and Poisson Tops 10.10 Closing Comments 10.11 Exercises Part IV Systems of Particles and Rigid Bodies 11 The Dynamics of Systems of Particles and Rigid Bodies 11.1 Introduction 11.2 Preliminaries 11.3 A Planar Double Pendulum 11.4 A Particle on a Rotating Circular Hoop 11.5 Constraints 11.6 A Canonical Function 11.7 Integrability Criteria 11.8 Constraint Forces and Constraint Moments 11.9 Potential Energies, Conservative Forces, and Conservative Moments 11.10 Lagrange’s Equations of Motion 11.11 Two Pin-Jointed Rigid Bodies 11.12 A Simple Model for a Spherical Robot 11.13 A Semicircular Cylinder Rolling on a Cart 11.14 A Single-Axis Rate Gyroscope 11.15 Orthogonality of Generalized Forces and Gimbal Lock 11.16 Closing Comments 11.17 Exercises Appendix A Background on Tensors A.1 Introduction A.2 Preliminaries: Bases, Alternators, and Kronecker Deltas A.3 The Tensor Product of Two Vectors A.4 Second-Order Tensors A.5 A Representation Theorem for Second-Order Tensors A.6 Functions of Second-Order Tensors A.7 Third-Order Tensors A.8 Special Types of Second-Order Tensors A.9 Derivatives of Tensors A.10 Exercises References Index