Advanced Dynamics: Analytical and Numerical Calculations with MATLAB

Cover

Advanced Dynamics - Analytical and Numerical Calculations with MATLAB

ISBN 9781461434740 e-ISBN 9781461434757

Preface

Contents

Chapter 1 Vector Algebra

  1.1 Terminology and Notation
  1.2 Position Vector
  1.3 Scalar (Dot) Product of Vectors
  1.4 Vector (Cross) Product of Vectors
  1.5 Scalar Triple Product of Three Vectors
  1.6 Vector Triple Product of Three Vector
  1.7 Derivative of a Vector Function
  1.8 Cauchy's Inequality, Lagrange's Identity, and Triangle Inequality
  1.9 Coordinate Transformation
  1.10 Tensors
      1.10.1 Operations with Tensors
      1.10.2 Some Further Properties of Second-Order Tensor
  1.11 Examples
  1.12 Problems
  1.13 Program

Chapter 2 Centroids and Moments of Inertia

  2.1 Centroids and Center of Mass
      2.1.1 First Moment and Centroid of a Set of Points
      2.1.2 Centroid of a Curve, Surface, or Solid
      2.1.3 Mass Center of a Set of Particles
      2.1.4 Mass Center of a Curve, Surface, or Solid
      2.1.5 First Moment of an Area
      2.1.6 Center of Gravity
      2.1.7 Theorems of Guldinus-Pappus
  2.2 Moments of Inertia
      2.2.1 Introduction
      2.2.2 Translation of Coordinate Axes
      2.2.3 Principal Axes
      2.2.4 Ellipsoid of Inertia
      2.2.5 Moments of Inertia for Areas
  2.3 Examples
  2.4 Problems

Chapter 3 Kinematics of a Particle

  3.1 Introduction
      3.1.1 Position, Velocity, and Acceleration
      3.1.2 Angular Motion of a Line
      3.1.3 Rotating Unit Vector
  3.2 Rectilinear Motion
  3.3 Curvilinear Motion
      3.3.1 Cartesian Coordinates
      3.3.2 Normal and Tangential Coordinates
      3.3.3 Circular Motion
      3.3.4 Polar Coordinates
      3.3.5 Cylindrical Coordinates
  3.4 Relative Motion
  3.5 Frenet's Formulas
  3.6 Examples
  3.7 Problems

Chapter 4 Dynamics of a Particle

  4.1 Newton's Second Law
  4.2 Newtonian Gravitation
  4.3 Inertial Reference Frames
  4.4 Cartesian Coordinates
      4.4.1 Projectile Problem
      4.4.2 Straight Line Motion
  4.5 Normal and Tangential Components
  4.6 Polar and Cylindrical Coordinates
  4.7 Principle of Work and Energy
  4.8 Work and Power
      4.8.1 Work Done on a Particle by a Linear Spring
      4.8.2 Work Done on a Particle by Weight
  4.9 Conservation of Energy
      4.9.1 Exercise
      4.9.2 Exercise
  4.10 Conservative Forces
      4.10.1 Potential Energy of a Force Exerted by a Spring
      4.10.2 Potential Energy of Weight
      4.10.3 Exercise
      4.10.4 Exercise
  4.11 Principle of Impulse and Momentum
  4.12 Conservation of Linear Momentum
  4.13 Principle of Angular Impulse and Momentum
  4.14 Examples
  4.15 Problems

Chapter 5 Kinematics of Rigid Bodies

  5.1 Introduction
  5.2 Velocity Analysis for a Rigid Body
  5.3 Acceleration Analysis for a Rigid Body
      5.3.1 Translation
      5.3.2 Rotation
      5.3.3 Helical Motion
      5.3.4 Planar Motion
  5.4 Angular Velocity Vector of a Rigid Body
  5.5 Motion of a Point that Moves Relative to a Rigid Body
  5.6 Planar Instantaneous Center
  5.7 Fixed and Moving Centrodes
  5.8 Closed Loop Equations
      5.8.1 Closed Loop Velocity Equations
      5.8.2 Closed Loop Acceleration Equations
  5.9 Independent Closed Loops Method
  5.10 Closed Kinematic Chains with MATLAB Functions
      5.10.1 Driver Link
      5.10.2 Position Analysis
      5.10.3 Complete Rotation of the Driver Link
      5.10.4 Velocity and Acceleration Analysis
  5.11 Examples
  5.12 Problems

Chapter 6 Dynamics of Rigid Bodies

  6.1 Equation of Motion for the Mass Center
  6.2 Linear Momentum and Angular Momentum
  6.3 Spatial Angular Momentum of a Rigid Body
  6.4 Kinetic Energy of a Rigid Body
  6.5 Equations of Motion
  6.6 Euler's Equations of Motion
  6.7 Motion of a Rigid Body About a Fixed Point
  6.8 Rotation of a Rigid Body About a Fixed Axis
  6.9 Plane Motion of Rigid Body
      6.9.1 D'Alembert's Principle
      6.9.2 Free-Body Diagrams
  6.10 Examples
  6.11 Problems

Chapter 7 Analytical Dynamics

  7.1 Introduction
  7.2 Equations of Motion
  7.3 Hamilton's Equations
  7.4 Poisson Bracket
  7.5 Rotation Transformation
  7.6 Examples
  7.7 Problems

References

Index