Physical description 
1 online resource. 
Series 
Solid mechanics and its applications, 09250042 ; volume 254


Solid mechanics and its applications ; v. 254.


Springer Engineering eBooks 2019 English+International

Bibliography 
Includes bibliographical references and index. 
Contents 
1 Basic Elements of Dynamics 1.1 Introduction1.2 Systems of Units1.3 Describing Motion in Different Coordinate Systems 1.3.1 Cartesian (Rectangular) Coordinates 1.3.2 Cylindrical and Polar Coordinates 1.3.3 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 Particle 2.1 Governing Equations 2.2 The Dynamics of Unconstrained Motion of a Particle 2.2.1 Equations of Motion 2.2.2 A Projectile Problem 2.2.3 Potential Energy 2.2.4 Kinetic Energy and Conservative Systems 2.2.5 WorkEnergy 2.2.6 A Projectile Problem with Drag Forces 2.3 The Dynamics of Constrained Motion of a Particle 2.3.1 Constrained Motion of a Bead on a Wire 2.3.2 A RollerCoaster Problem 2.4 Constraints and Equations of Motion  A Matrix Approach 2.4.1 Types of Constraints 2.4.2 Constraints for Motion in Three Dimensions 2.4.3 Augmented Solutions for Ideal Constraint Forces and the Equations of Motion in Cartesian Coordinates 2.5 Constraints and Equations of Motion in Generalized Coordinates 2.5.1 Solutions in Generalized Coordinates 2.5.2 Unconstrained Motion of a SpringPendulum 2.5.3 Constrained Motion of a Pendulum 2.5.4 Constraints and the Motion of the Planets 2.6 Generalized Coordinates and the Equations Motion  A Geometric Approach 2.6.1 Embedding of Constraints 2.6.2 Augmented Approach with Generalized Coordinates 2.7 Lagrange's Equations 2.7.1 Generalized Momenta and Ignorable Coordinates 2.8 Analytical Dynamics and Virtual Work 2.9 Other Principles and Virtual Quantities2.10 NonIdeal 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 Particles 3.1 Internal Forces 3.2 NewtonEuler Laws for a System of Particles 3.2.1 Motion of the Center of Mass 3.2.2 Impulse and Linear Momentum 3.2.3 The Moment Equation and Angular Momentum 3.2.4 Angular Impulse and Angular Momentum 3.2.5 Work and Energy3.2.5.1 Kinetic Energy and Angular Momentum for a Rigid System of Particles3.2.5.2 WorkKinetic Energy for an Elastically Connected System of Particles 3.3 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 Pendulum 3.5 A NonHolonomic Constrained System of Particles 3.6 Dependent Constraints3.7 Problems3.8 References 4 Kinematics and Relative Motion 4.1 Relative Velocity and Acceleration 4.1.1 Relative Motion  Cylindrical and Spherical Coordinates 4.2 Relative Motion and the Transport Theorem 4.2.1 Relative Velocity and Acceleration  More Explicit Forms 4.2.2 Relative Motion for Rigid Bodies 4.2.3 The Analysis of Kinematically Driven Systems  I 4.2.4 Singular Configurations 4.2.5 Numerical Solution of the Position Equations 4.2.6 Velocity and Acceleration Constraints 4.2.7 The Analysis of Kinematically Driven Systems  II 4.3 Motion on the Rotating Earth 4.4 Matrix Kinematics of Rigid Body Planar Motion 4.4.1 Positional Analysis 4.4.2 Velocity Analysis 4.4.3 Acceleration Analysis 4.4.4 General Relative Velocity and Acceleration Relations 4.5 MatrixVector Kinematics of Constraints and Kinematically Driven Systems 4.6 ThreeDimensional Motion  Finite Rotations and Relative Position 4.7 Angular Velocity and Relative Velocity 4.8 Angular Velocity and Euler Angles 4.9 Acceleration and the Equations of Motion 4.10 Euler Parameters 4.11 The Commonly Used Euler Angle Sets 4.12 Problems 4.13 References 5 Planar Dynamics of Rigid Bodies 5.1 Governing Equations for a Rigid Body in Plane Motion 5.1.1 A System of Rigid Bodies in Plane Motion 5.2 Moment of Inertia 5.3 Planar Problems and Constraint Forces 5.3.1 A NewtonEuler Approach 5.3.2 An Augmented Approach 5.3.3 Rolling without Slipping 5.4 Kinetic Energy and WorkEnergy 5.4.1 Kinetic Energy of a Rigid Body in Plane Motion 5.4.2 WorkEnergy Principle for a Rigid Body in Plane Motion 5.5 Angular Momentum and the Moment Equation 5.5.1 Motion Relative to a Point that Moves with a Rigid Body 5.5.2 Motion Relative to a General Point 5.6 Solving Systems of Rigid Bodies in Plane Motion 5.6.1 Lagrange's Equations 5.7 Problems 6 Dynamic and Static Stability 6.1 Dynamic Stability 6.2 Stability of a Natural, Conservative System Near Equilibrium 6.3 Stability of a NonNatural System Near Equilibrium 6.4 Stability Analysis through Linearization 6.5 Static Stability 6.6 Bifurcations and Buckling6.7 Limit Load Instability 6.8 SnapThrough Instability 6.9 Problems 6.10 References 7 Vibrations of Dynamical Systems 7.1 An Overview of Linearized Vibrating Systems 7.2 Linearized Motion Near Equilibrium 7.3 Free Vibrations without Damping 7.4 Forced Vibrations without Damping 7.4.1 Harmonic Driving Forces 7.5 Free Vibrations with Damping 7.6 Forced Vibration with Damping 7.6.1 Harmonic Driving Forces 7.6.1 System Impulse Response 7.6.2 Convolution Integrals 7.7 Problems 8 General Spatial Dynamics of Rigid Bodies 8.1 Angular Momentum 8.1.1 Angular Momentum About a BodyFixed Point 8.1.2 Angular Momentum About a General Point 8.2 Kinetic Energy 8.3 ImpulseMomentum and WorkEnergy Principles for a Rigid Body 8.4 NewtonEuler Equations of Motion 8.4.1 Governing Equations  General Case 8.4.2 Governing Equations for a Rigid Body  Use of a BodyFixed Point 8.5 Solutions of Euler's Equations for Rotational Motion 8.6 Rotational Motion and the Euler Parameters Constraint 8.7 Solving Systems of Rigid Bodies 8.7.1 Lagrange's Equations 8.8 The Rolling Disk 8.9 Problems 8.10 References 9 Dynamics of Deformable Bodies 9.1 Longitudinal Wave Motion 9.1.1 The Method of Finite Differences 9.1.2 The Finite Element Method 9.2 Problems Appendices A Matrices A.1 Basic Matrix Algebra A.2 Vectors as Matrices A.3 Determinants and Cofactors A.4 Inverses and Solutions of Linear Equations A.5 References B Mass Moments and Products of Inertia B.1 Definitions B.2 Parallel Axis Theorem B.3 Rotation of Axes B.4 Principal Moments of Inertia B.5 Some Moments of Inertia C Numerical Methods C.1 Numerical Solutions of Ordinary Differential Equations C.2 Numerical Solutions of NonLinear Algebraic Equations D Vibrations of One Degree of Freedom Systems D.1 General Solutions D.1.1 Homogeneous Solutions D.1.2 Free Vibration Solutions D.1.3 Impulse Response and a Particular Solution as a Convolution Integral D.1.4 The SteadyState Response of One Degree of Freedom Systems D.1.5 Combining Homogeneous and Particular Solutions D.2 References E Fourier Transforms E.1 Fourier Transforms and Discrete Fourier Transforms E.2 Fast Fourier Transforms and Numerical Fourier Analysis E.3 Different Forms of the Fourier Transform F MATLAB® Functions and Scripts. 
Other author 
SpringerLink issuing body.

Subject 
Dynamics.


Mechanics.


Electronic books. 
ISBN 
9783319984704 (electronic bk.) 

3319984705 (electronic bk.) 

9783319984698 (print) 
