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Dynamics of Particles and Rigid Bodies A Systematic Approach 1st Edition by Anil Rao ISBN 0521858119 9780521858113

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Author(s): Anil Rao
ISBN(s): 9780521858113, 0521858119
Edition: CUP
File Details: PDF, 6.34 MB
Year: 2005
Language: english
SKU: EB-1014676 Category: Tag:

Dynamics of Particles and Rigid Bodies A Systematic Approach 1st Edition by Anil Rao – Ebook PDF Instant Download/Delivery: 0521858119, 9780521858113
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ISBN 10: 0521858119 
ISBN 13: 9780521858113
Author: Anil Rao

This 2006 book is intended for undergraduate courses in dynamics. The work is a unique blend of conceptual, theoretical, and practical aspects of dynamics generally not found in dynamics books at the undergraduate level. In particular, in this book the concepts are developed in a highly rigorous manner and are applied to examples using a step-by-step approach that is completely consistent with the theory. In addition, for clarity, the notation used to develop the theory is identical to that used to solve example problems. The result of this approach is that a student is able to see clearly the connection between the theory and the application of theory to example problems. While the material is not new, instructors and their students will appreciate the highly pedagogical approach that aids in the mastery and retention of concepts. The approach used in this book teaches a student to develop a systematic approach to problem-solving.

Dynamics of Particles and Rigid Bodies A Systematic Approach 1st Table of contents:

Chapter 1: Introductory Concepts

  • 1.1 Scalars

  • 1.2 Vectors

    • 1.2.1 Types of Vectors

    • 1.2.2 Addition of Vectors

    • 1.2.3 Components of a Vector

    • 1.2.4 Multiplication of a Vector by a Scalar

    • 1.2.5 Scalar Product

    • 1.2.6 Vector Product

    • 1.2.7 Scalar Triple Product

    • 1.2.8 Vector Triple Product

  • 1.3 Tensors

    • 1.3.1 Important Classes of Tensors

    • 1.3.2 Tensor Product Between Vectors

    • 1.3.3 Basis Representations of Tensors

  • 1.4 Matrices

    • 1.4.1 Systems of Linear Equations

    • 1.4.2 Classes of Matrices

    • 1.4.3 Relationship Between Tensors and Matrices

    • 1.4.4 Transformation of Column-Vectors and Row-Vectors

    • 1.4.5 Transformation of Matrices

    • 1.4.6 Eigenvalues and Eigenvectors

    • 1.4.7 Eigenvalues and Eigenvectors of a Real-Symmetric Matrix

  • 1.5 Ordinary Differential Equations

Chapter 2: Kinematics

  • 2.1 Reference Frames

    • 2.1.1 Definition of a Reference Frame and an Observer

    • 2.1.2 Invariance of Space and Time in Different Reference Frames

    • 2.1.3 Inertial and Noninertial Reference Frames

  • 2.2 Coordinate Systems

  • 2.3 Rate of Change of Scalar and Vector Functions

    • 2.3.1 Rate of Change of a Scalar Function

    • 2.3.2 Rate of Change of a Vector Function

    • 2.3.3 Rate of Change of a Scalar Function of a Vector

    • 2.3.4 Rates of Change of Common Functions of Vectors

  • 2.4 Position, Velocity, and Acceleration

  • 2.5 Degrees of Freedom of a Particle

  • 2.6 Relative Position, Velocity, and Acceleration

  • 2.7 Rectilinear Motion

    • Case 1: Acceleration as a Function of Time

    • Case 2: Acceleration as a Function of Velocity

    • Case 3: Acceleration as a Function of Position

  • 2.8 Using Noninertial Reference Frames to Describe Motion

  • 2.9 Rate of Change of a Vector in a Rotating Reference Frame

    • 2.9.1 Further Explanation of the Transport Theorem

    • 2.9.2 Addition of Angular Velocities

    • 2.9.3 Angular Acceleration

  • 2.10 Kinematics in a Rotating Reference Frame

  • 2.11 Common Coordinate Systems

    • 2.11.1 Cartesian Coordinates

    • 2.11.2 Cylindrical Coordinates

    • 2.11.3 Spherical Coordinates

    • 2.11.4 Intrinsic Coordinates

  • 2.12 Kinematics in a Rotating and Translating Reference Frame

  • 2.13 Practical Approach to Computing Velocity and Acceleration

  • 2.14 Kinematics of a Particle in Continuous Contact with a Surface

  • 2.15 Kinematics of Rigid Bodies

    • 2.15.1 Configuration and Degrees of Freedom of a Rigid Body

    • 2.15.2 Rigid Body Motion Using Body-Fixed Coordinate Systems

    • 2.15.3 Translational Kinematics of Points on a Rigid Body

    • 2.15.4 Kinematics of Rolling and Sliding Rigid Bodies

      • Rolling and Sliding Between Two Moving Rigid Bodies

      • Rolling and Sliding of a Rigid Body Along a Fixed Surface

      • Independence of Relative Velocity with Respect to Reference Frame During Sliding

    • 2.15.5 Orientation of a Rigid Body: Eulerian Angles

      • Type I Euler Angles

      • Euler Basis and Dual Euler Basis

  • Summary of Chapter 2

  • Problems for Chapter 2

Chapter 3: Kinetics of Particles

  • 3.1 Forces Commonly Used in Dynamics

    • 3.1.1 Contact Forces

      • Decomposition of a Contact Force Applied by a Surface

      • Reaction Force Exerted by a Surface on a Particle

      • Reaction Force Exerted by a Curve on a Particle

      • Friction Force Exerted by a Surface on a Particle

      • Coulomb Friction

      • Viscous Friction

    • 3.1.2 Spring Forces

      • Linear Spring Forces

      • Case 1: …

      • Case 2: …

      • Curvilinear Spring

    • 3.1.3 Central Forces

    • 3.1.4 Gravitational Forces

      • Newton’s Law of Gravitation

    • 3.1.5 Force of Gravity

  • 3.2 Inertial Reference Frames

  • 3.3 Newton’s Laws for a Particle

  • 3.4 Comments on Newton’s Laws

  • 3.5 Examples of Application of Newton’s Laws in Particle Dynamics

  • 3.6 Linear Momentum and Linear Impulse for a Particle

    • 3.6.1 Linear Momentum of a Particle

    • 3.6.2 Principle of Linear Impulse and Momentum for a Particle

    • 3.6.3 Conservation of Linear Momentum

  • 3.7 Moment of a Force and Moment Transport Theorem for a Particle

  • 3.8 Angular Momentum and Angular Impulse for a Particle

    • 3.8.1 Angular Momentum and Its Rate of Change of a Particle

    • 3.8.2 Principle of Angular Impulse and Angular Momentum of a Particle

    • 3.8.3 Conservation of Angular Momentum

  • 3.9 Instantaneous Linear and Angular Impulse

  • 3.10 Power, Work, and Energy for a Particle

    • 3.10.1 Power and Work of a Force

    • 3.10.2 Kinetic Energy and Work-Energy Theorem for a Particle

    • 3.10.3 Principle of Work and Energy for a Particle

    • 3.10.4 Conservative Forces and Potential Energy

    • 3.10.5 Examples of Conservative Forces

      • Constant Forces

      • Spring Forces

      • Gravitational Forces

    • 3.10.6 Alternate Form of Work-Energy Theorem for a Particle

    • 3.10.7 Conservation of Energy for a Particle

    • 3.10.8 Alternate Form of the Principle of Work and Energy for a Particle

  • Summary of Chapter 3

  • Problems for Chapter 3

Chapter 4: Kinetics of a System of Particles

  • 4.1 Center of Mass and Linear Momentum of a System of Particles

    • 4.1.1 Center of Mass of a System of Particles

    • 4.1.2 Linear Momentum of a System of Particles

  • 4.2 Angular Momentum of a System of Particles

  • 4.3 Newton’s 2nd Law for a System of Particles

  • 4.4 Moment of a System of Forces Acting on a System of Particles

  • 4.5 Rate of Change of Angular Momentum for a System of Particles

  • 4.6 Impulse and Momentum for a System of Particles

    • 4.6.1 Linear Impulse and Linear Momentum for a System of Particles

    • 4.6.2 Angular Impulse and Angular Momentum for a System of Particles

  • 4.7 Work and Energy for a System of Particles

    • 4.7.1 Kinetic Energy for a System of Particles

    • 4.7.2 Work-Energy Theorem for a System of Particles

    • 4.7.3 Alternate Form of Work-Energy Theorem for a System of Particles

  • 4.8 Collision of Particles

    • 4.8.1 Collision Model

      • Application of Linear Impulse and Linear Momentum During Compression

      • Application of Linear Impulse and Linear Momentum During Restitution

      • Application of Linear Impulse and Linear Momentum During Entire Collision

      • Solving for Post-Collision Velocities

    • 4.8.2 Further Discussion About Collision Model

  • Summary of Chapter 4

  • Problems for Chapter 4

Chapter 5: Kinetics of Rigid Bodies

  • 5.1 Center of Mass and Linear Momentum of a Rigid Body

    • 5.1.1 Center of Mass of a Rigid Body

    • 5.1.2 Linear Momentum of a Rigid Body

  • 5.2 Angular Momentum of a Rigid Body

  • 5.3 Moment of Inertia Tensor of a Rigid Body

    • 5.3.1 Moment of Inertia Tensor Relative to a Body-Fixed Point

    • 5.3.2 Moment of Inertia Tensor Relative to Center of Mass

    • 5.3.3 Moments and Products of Inertia

    • 5.3.4 Parallel-Axis Theorem (Huygens-Steiner Theorem)

    • 5.3.5 Limitation of the Parallel-Axis Theorem

    • 5.3.6 Limitation of Moment of Inertia Form of Angular Momentum

  • 5.4 Principal-Axis Coordinate Systems

    • 5.4.1 Rotation About a Principal Axis

    • 5.4.2 Determination of a Principal-Axis Basis

    • 5.4.3 Common Usage of Principal-Axis Coordinate Systems

  • 5.5 Actions on a Rigid Body

    • 5.5.1 Force Applied to a Rigid Body

    • 5.5.2 Pure Torque Applied to a Rigid Body

    • 5.5.4 Conservative Torques

  • 5.6 Moment Transport Theorem for a Rigid Body

  • 5.7 Euler’s Laws for a Rigid Body

    • 5.7.1 Euler’s 1st Law

    • 5.7.2 Euler’s 2nd Law

    • 5.7.3 Alternate Forms of Euler’s 2nd Law

      • Euler’s 2nd Law Relative to an Arbitrary Reference Point

      • Euler’s 2nd Law Relative to the Center of Mass

    • 5.7.4 Important Results About Euler’s 2nd Law

  • 5.8 Systems of Rigid Bodies

  • 5.9 Rotational Dynamics of a Rigid Body Using Moment of Inertia

    • 5.9.1 Euler’s 2nd Law in Terms of Moment of Inertia Tensor

    • 5.9.2 Euler’s Equations for a Rigid Body

    • 5.9.3 Stability of Rotational Motion About a Principal Axis

  • 5.10 Work and Energy for a Rigid Body

    • 5.10.1 Kinetic Energy of a Rigid Body

    • 5.10.2 Work-Energy Theorem for a Rigid Body

    • 5.10.3 Principle of Work and Energy for a Rigid Body

    • 5.10.4 Alternate Form of Work-Energy Theorem for a Rigid Body

    • 5.10.5 Conservation of Energy for a Rigid Body

    • 5.10.6 Alternate Form of Principle of Work and Energy for a Rigid Body

  • 5.11 Impulse and Momentum for a Rigid Body

    • 5.11.1 Linear Impulse and Linear Momentum for a R

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Tags: Anil Rao, Dynamics, Rigid Bodies, Systematic