Computational Dynamics 3e
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Computational Dynamics, 3rd edition, thoroughly revised and updated, provides logical coverage of both theory and numerical computation techniques for practical applications.

The author introduces students to this advanced topic covering the concepts, definitions and techniques used in multi-body system dynamics including essential coverage of kinematics and dynamics of motion in three dimensions. He uses analytical tools including Lagrangian and Hamiltonian methods as well as Newton-Euler Equations.

An educational version of multibody computer code is now included in this new edition that can be used for instruction and demonstration of the theories and formulations presented in the book, and a new chapter is included to explain the use of this code in solving practical engineering problems.

Most books treat the subject of dynamics from an analytical point of view, focusing on the techniques for analyzing the problems presented. This book is exceptional in that it covers the practical computational methods used to solve "real-world" problems. This makes it of particular interest not only for senior/ graduate courses in mechanical and aerospace engineering, but also to professional engineers.

  • Modern and focused treatment of the mathematical techniques, physical theories and application of rigid body mechanics that emphasizes the fundamentals of the subject, stresses the importance of computational methods and offers a wide variety of examples.
  • Each chapter features simple examples that show the main ideas and procedures, as well as straightforward problem sets that facilitate learning and help readers build problem-solving skills


Ahmed Shabana, University of Illinois, USA, is the Richard & Loan Hill Professor of Engineering in the Department of Mechanical Engineering at the University of Illinois at Chicago. He is the author of a number of books, including Dynamics of Multibody Systems, Vibration of Discrete and Continuous Systems, and Theory of Vibration: An Introduction.



1 Introduction.

1.1 Computational Dynamics.

1.2 Motion and Constraints.

1.3 Degrees of Freedom.

1.4 Kinematic Analysis.

1.5 Force Analysis.

1.6 Dynamic Equations and Their Different Forms.

1.7 Forward and Inverse Dynamics.

1.8 Planar and Spatial Dynamics.

1.9 Computer and Numerical Methods.

1.10 Organization, Scope, and Notations of the Book.

2 Linear Algebra.

2.1 Matrices.

2.2 Matrix Operations.

2.3 Vectors.

2.4 Three-Dimensional Vectors.

2.5 Solution of Algebraic Equations.

2.6 Triangular Factorization.

2.7 QR Decomposition.

2.8 Singular Value Decomposition.


3 Kinematics.

3.1 Kinematics of Rigid Bodies.

3.2 Velocity Equations.

3.3 Acceleration Equations.

3.4 Kinematics of a Point Moving on a Rigid Body.

3.5 Constrained Kinematics.

3.6 Classical Kinematic Approach.

3.7 Computational Kinematic Approach.

3.8 Formulation of the Driving Constraints.

3.9 Formulation of the Joint Constraints.

3.10 Computational Methods in Kinematics.

3.11 Computer Implementation.

3.12 Kinematic Modeling and Analysis.

3.13 Concluding Remarks.


4 Forms of the Dynamic Equations.

4.1 D’Alembert’s Principle.

4.2 D’Alembert’s Principle and Newton–Euler Equations.

4.3 Constrained Dynamics.

4.4 Augmented Formulation.

4.5 Lagrange Multipliers.

4.6 Elimination of the Dependent Accelerations.

4.7 Embedding Technique.

4.8 Amalgamated Formulation.

4.9 Open-Chain Systems.

4.10 Closed-Chain Systems.

4.11 Concluding Remarks.


5 Virtual Work and Lagrangian Dynamics.

5.1 Virtual Displacements.

5.2 Kinematic Constraints and Coordinate Partitioning.

5.3 Virtual Work.

5.4 Examples of Force Elements.

5.5 Workless Constraints.

5.6 Principle of Virtual Work in Statics.

5.7 Principle of Virtual Work in Dynamics.

5.8 Lagrange’s Equation.

5.9 Gibbs–Appel Equation.

5.10 Hamiltonian Formulation.

5.11 Relationship between Virtual Work and Gaussian Elimination.


6 Constrained Dynamics.

6.1 Generalized Inertia.

6.2 Mass Matrix and Centrifugal Forces.

6.3 Equations of Motion.

6.4 System of Rigid Bodies.

6.5 Elimination of the Constraint Forces.

6.6 Lagrange Multipliers.

6.7 Constrained Dynamic Equations.

6.8 Joint Reaction Forces.

6.9 Elimination of Lagrange Multipliers.

6.10 State Space Representation.

6.11 Numerical Integration.

6.12 Algorithm and Sparse Matrix Implementation.

6.13 Differential and Algebraic Equations.

6.14 Inverse Dynamics.

6.15 Static Analysis.


7 Spatial Dynamics.

7.1 General Displacement.

7.2 Finite Rotations.

7.3 Euler Angles.

7.4 Velocity and Acceleration.

7.5 Generalized Coordinates.

7.6 Generalized Inertia Forces.

7.7 Generalized Applied Forces.

7.8 Dynamic Equations of Motion.

7.9 Constrained Dynamics.

7.10 Formulation of the Joint Constraints.

7.11 Newton–Euler Equations.

7.12 D’Alembert’s Principle.

7.13 Linear and Angular Momentum.

7.14 Recursive Methods.


8 Special Topics in Dynamics.

8.1 Gyroscopes and Euler Angles.

8.2 Rodriguez Formula.

8.3 Euler Parameters.

8.4 Rodriguez Parameters.

8.5 Quaternions.

8.6 Rigid Body Contact.

8.7 Stability and Eigenvalue Analysis.


9 Multibody Sysyem Computer Codes.

9.1 Introduction to SAMS/2000.

9.2 Code Structure.

9.3 System Identification and Data Structure.

9.4 Installing the Code and Theoretical Background.

9.5 SAMS/2000 Setup.

9.6 Use of the Code.

9.7 Body Data.

9.8 Constraint Data.

9.9 Performing Simulations.

9.10 Batch Jobs.

9.11 Graphics Control.

9.12 Animation Capabilities.

9.13 General Use of the Input Data Panels.

9.14 Spatial Analysis.

9.15 Special Modules and Features of the Code.