Engineering Dynamics 2.0: Fundamentals and Numerical Solutions

1 Basic Elements of Dynamics
1.1 Introduction1.2 Systems of Units1.3 Describing Motion in Different Coordinate Systems1.3.1 Cartesian (Rectangular) Coordinates1.3.2 Cylindrical and Polar Coordinates1.3.3 Spherical Coordinates1.4 Vectors and Matrices1.5 Angular Velocity and the Time Derivative of Unit Vectors1.6 Objective and Organization of the Book1.7 Problems
2 Dynamics of a Particle2.1 Governing Equations2.2 The Dynamics of Unconstrained Motion of a Particle 2.2.1 Equations of Motion2.2.2 A Projectile Problem2.2.3 Potential Energy2.2.4 Kinetic Energy and Conservative Systems2.2.5 Work-Energy2.2.6 A Projectile Problem with Drag Forces2.3 The Dynamics of Constrained Motion of a Particle2.3.1 Constrained Motion of a Bead on a Wire2.3.2 A Roller-Coaster Problem2.4 Constraints and Equations of Motion - A Matrix Approach2.4.1 Types of Constraints2.4.2 Constraints for Motion in Three Dimensions2.4.3 Augmented Solutions for Ideal Constraint Forces and the Equations of         Motion in Cartesian Coordinates2.5 Constraints and Equations of Motion in Generalized Coordinates2.5.1 Solutions in Generalized Coordinates2.5.2 Unconstrained Motion of a Spring-Pendulum2.5.3 Constrained Motion of a Pendulum2.5.4 Constraints and the Motion of the Planets2.6 Generalized Coordinates and the Equations Motion - A Geometric Approach2.6.1 Embedding of Constraints2.6.2 Augmented Approach with Generalized Coordinates2.7 Lagrange's Equations2.7.1 Generalized Momenta and Ignorable Coordinates2.8 Analytical Dynamics and Virtual Work2.9 Other Principles and Virtual Quantities2.10 Non-Ideal Constraint Forces2.11 Explicit Embedding of Constraints - A General Approach2.12 The Augmented Approach and Constraint Satisfaction2.13 Problems2.14 References
3 Dynamics of a System of Particles3.1 Internal Forces3.2 Newton-Euler Laws for a System of Particles3.2.1 Motion of the Center of Mass3.2.2 Impulse and Linear Momentum3.2.3 The Moment Equation and Angular Momentum 3.2.4 Angular Impulse and Angular Momentum3.2.5 Work and Energy3.2.5.1 Kinetic Energy and Angular Momentum for a Rigid System of Particles3.2.5.2 Work-Kinetic Energy for an Elastically Connected System of Particles3.3 Dynamics of a Rigidly Constrained System of Particles (Rigid Body)3.4 Equations of Motion in Generalized Coordinates 3.4.1 Motion of a Double Pendulum3.5 A Non-Holonomic Constrained System of Particles3.6 Dependent Constraints3.7 Problems3.8 References
4 Kinematics and Relative Motion4.1 Relative Velocity and Acceleration4.1.1 Relative Motion - Cylindrical and Spherical Coordinates4.2 Relative Motion and the Transport Theorem4.2.1 Relative Velocity and Acceleration - More Explicit Forms4.2.2 Relative Motion for Rigid Bodies4.2.3 The Analysis of Kinematically Driven Systems - I4.2.4 Singular Configurations4.2.5 Numerical Solution of the Position Equations4.2.6 Velocity and Acceleration Constraints4.2.7 The Analysis of Kinematically Driven Systems - II4.3 Motion on the Rotating Earth4.4 Matrix Kinematics of Rigid Body Planar Motion4.4.1 Positional Analysis4.4.2 Velocity Analysis4.4.3 Acceleration Analysis4.4.4 General Relative Velocity and Acceleration Relations4.5 Matrix-Vector Kinematics of Constraints and Kinematically Driven Systems4.6 Three-Dimensional Motion - Finite Rotations and Relative Position4.7 Angular Velocity and Relative Velocity4.8 Angular Velocity and Euler Angles4.9 Acceleration and the Equations of Motion4.10 Euler Parameters4.11 The Commonly Used Euler Angle Sets4.12 Problems4.13 References
5 Planar Dynamics of Rigid Bodies5.1 Governing Equations for a Rigid Body in Plane Motion5.1.1 A System of Rigid Bodies in Plane Motion5.2 Moment of Inertia5.3 Planar Problems and Constraint Forces5.3.1 A Newton-Euler Approach5.3.2 An Augmented Approach5.3.3 Rolling without Slipping5.4 Kinetic Energy and Work-Energy5.4.1 Kinetic Energy of a Rigid Body in Plane Motion5.4.2 Work-Energy Principle for a Rigid Body in Plane Motion5.5 Angular Momentum and the Moment Equation5.5.1 Motion Relative to a Point that Moves with a Rigid  Body5.5.2 Motion Relative to a General Point5.6 Solving Systems of Rigid Bodies in Plane Motion 5.6.1 Lagrange's Equations5.7 Problems
6 Dynamic and Static Stability6.1 Dynamic Stability6.2 Stability of a Natural, Conservative System Near Equilibrium6.3 Stability of a Non-Natural System Near Equilibrium6.4 Stability Analysis through Linearization6.5 Static Stability6.6 Bifurcations and Buckling6.7 Limit Load Instability6.8 Snap-Through Instability6.9 Problems6.10 References
7 Vibrations of Dynamical Systems7.1 An Overview of Linearized Vibrating Systems7.2 Linearized Motion Near Equilibrium7.3 Free Vibrations without Damping7.4 Forced Vibrations without Damping7.4.1 Harmonic Driving Forces7.5 Free Vibrations with Damping7.6 Forced Vibration with Damping7.6.1 Harmonic Driving Forces7.6.1 System Impulse Response 7.6.2 Convolution Integrals 7.7 Problems
8 General Spatial Dynamics of Rigid Bodies 8.1 Angular Momentum8.1.1 Angular Momentum About a Body-Fixed Point8.1.2 Angular Momentum About a General Point8.2 Kinetic Energy8.3 Impulse-Momentum and Work-Energy Principles for a Rigid Body8.4 Newton-Euler Equations of Motion8.4.1 Governing Equations -  General Case8.4.2 Governing Equations for a Rigid Body - Use of a Body-Fixed Point 8.5 Solutions of Euler's Equations for Rotational Motion8.6 Rotational Motion and the Euler Parameters Constraint8.7 Solving Systems of Rigid Bodies8.7.1 Lagrange's Equations8.8 The Rolling Disk8.9 Problems8.10 References
9 Dynamics of Deformable Bodies9.1 Longitudinal Wave Motion9.1.1 The Method of Finite Differences9.1.2 The Finite Element Method9.2 Problems
Appendices
A MatricesA.1 Basic Matrix AlgebraA.2 Vectors as MatricesA.3 Determinants and CofactorsA.4 Inverses and Solutions of Linear EquationsA.5 References
B Mass Moments and Products of InertiaB.1 DefinitionsB.2 Parallel Axis TheoremB.3 Rotation of AxesB.4 Principal Moments of InertiaB.5 Some Moments of Inertia
C Numerical MethodsC.1 Numerical Solutions of Ordinary Differential EquationsC.2 Numerical Solutions of Non-Linear Algebraic Equations
D Vibrations of One Degree of Freedom SystemsD.1 General SolutionsD.1.1 Homogeneous SolutionsD.1.2 Free Vibration SolutionsD.1.3 Impulse Response and a Particular Solution as a Convolution IntegralD.1.4 The Steady-State Response of One Degree of Freedom SystemsD.1.5 Combining Homogeneous and Particular Solutions D.2 References
E Fourier TransformsE.1 Fourier Transforms and Discrete Fourier TransformsE.2 Fast Fourier Transforms and Numerical Fourier AnalysisE.3 Different Forms of the Fourier Transform
F MATLAB® Functions and Scripts