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Advanced Dynamics: Rigid Body, Multibody, and Aerospace Applications

ISBN: 978-0-470-39835-7
1344 pages
March 2011
Advanced Dynamics: Rigid Body, Multibody, and Aerospace Applications (0470398353) cover image


A thorough understanding of rigid body dynamics as it relates to modern mechanical and aerospace systems requires engineers to be well versed in a variety of disciplines. This book offers an all-encompassing view by interconnecting a multitude of key areas in the study of rigid body dynamics, including classical mechanics, spacecraft dynamics, and multibody dynamics. In a clear, straightforward style ideal for learners at any level, Advanced Dynamics builds a solid fundamental base by first providing an in-depth review of kinematics and basic dynamics before ultimately moving forward to tackle advanced subject areas such as rigid body and Lagrangian dynamics. In addition, Advanced Dynamics:

  • Is the only book that bridges the gap between rigid body, multibody, and spacecraft dynamics for graduate students and specialists in mechanical and aerospace engineering
  • Contains coverage of special applications that highlight the different aspects of dynamics and enhances understanding of advanced systems across all related disciplines
  • Presents material using the author's own theory of differentiation in different coordinate frames, which allows for better understanding and application by students and professionals

Both a refresher and a professional resource, Advanced Dynamics leads readers on a rewarding educational journey that will allow them to expand the scope of their engineering acumen as they apply a wide range of applications across many different engineering disciplines.

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Table of Contents


Part I Fundamentals.

1 Fundamentals of Kinematics.

1.1 Coordinate Frame and Position Vector.

1.2 Vector Algebra.

1.3 Orthogonal Coordinate Frames.

1.4 Differential Geometry.

1.5 Motion Path Kinematics.

1.6 Fields.

2 Fundamentals of Dynamics.

2.1 Laws of Motion.

2.2 Equation of Motion.

2.3 Special Solutions.

2.4 Spatial and Temporal Integrals.

2.5 Application of Dynamics.

Part II Geometric Kinematics.

3 Coordinate Systems.

3.1 Cartesian Coordinate System.

3.2 Cylindrical Coordinate System.

3.3 Spherical Coordinate System.

3.4 Nonorthogonal Coordinate Frames.

3.5 Curvilinear Coordinate System.

4 Rotation Kinematics.

4.1 Rotation About Global Cartesian Axes.

4.2 Successive Rotations About Global Axes.

4.3 Global Roll–Pitch–Yaw Angles.

4.4 Rotation About Local Cartesian Axes.

4.5 Successive Rotations About Local Axes.

4.6 Euler Angles.

4.7 Local Roll–Pitch–Yaw Angles.

4.8 Local versus Global Rotation.

4.9 General Rotation.

4.10 Active and Passive Rotations.

4.11 Rotation of Rotated Body.

5 Orientation Kinematics.

5.1 Axis–Angle Rotation.

5.2 Euler Parameters.

5.3 Quaternion.

5.4 Spinors and Rotators.

5.5 Problems in Representing Rotations.

5.6 Composition and Decomposition of Rotations.

6 Motion Kinematics.

6.1 Rigid-Body Motion.

6.2 Homogeneous Transformation.

6.3 Inverse and Reverse Homogeneous Transformation.

6.4 Compound Homogeneous Transformation.

6.5 Screw Motion.

6.6 Inverse Screw.

6.7 Compound Screw Transformation.

6.8 Plücker Line Coordinate.

6.9 Geometry of Plane and Line.

6.10 Screw and Plucker Coordinate.

7 Multibody Kinematics.

7.1 Multibody Connection.

7.2 Denavit–Hartenberg Rule.

7.3 Forward Kinematics.

7.4 Assembling Kinematics.

7.5 Order-Free Rotation.

7.6 Order-Free Transformation.

7.7 Forward Kinematics by Screw.

7.8 Caster Theory in Vehicles.

7.9 Inverse Kinematics.

Part III Derivative Kinematics.

8 Velocity Kinematics.

8.1 Angular Velocity.

8.2 Time Derivative and Coordinate Frames.

8.3 Multibody Velocity.

8.4 Velocity Transformation Matrix.

8.5 Derivative of a Homogeneous Transformation Matrix.

8.6 Multibody Velocity.

8.7 Forward-Velocity Kinematics.

8.8 Jacobian-Generating Vector.

8.9 Inverse-Velocity Kinematics.

9 Acceleration Kinematics.

9.1 Angular Acceleration.

9.2 Second Derivative and Coordinate Frames.

9.3 Multibody Acceleration.

9.4 Particle Acceleration.

9.5 Mixed Double Derivative.

9.6 Acceleration Transformation Matrix.

9.7 Forward-Acceleration Kinematics.

9.8 Inverse-Acceleration Kinematics.

10 Constraints.

10.1 Homogeneity and Isotropy.

10.2 Describing Space.

10.3 Holonomic Constraint.

10.4 Generalized Coordinate.

10.5 Constraint Force.

10.6 Virtual and Actual Works.

10.7 Nonholonomic Constraint.

10.8 Differential Constraint.

10.9 Generalized Mechanics.

10.10 Integral of Motion.

10.11 Methods of Dynamics.

Part IV Dynamics.

11 Rigid Body and Mass Moment.

11.1 Rigid Body.

11.2 Elements of the Mass Moment Matrix.

11.3 Transformation of Mass Moment Matrix.

11.4 Principal Mass Moments.

12 Rigid-Body Dynamics.

12.1 Rigid-Body Rotational Cartesian Dynamics.

12.2 Rigid-Body Rotational Eulerian Dynamics.

12.3 Rigid-Body Translational Dynamics.

12.4 Classical Problems of Rigid Bodies.

12.5 Multibody Dynamics.

12.6 Recursive Multibody Dynamics.

13 Lagrange Dynamics.

13.1 Lagrange Form of Newton Equations.

13.2 Lagrange Equation and Potential Force.

13.3 Variational Dynamics.

13.4 Hamilton Principle.

13.5 Lagrange Equation and Constraints.

13.6 Conservation Laws.

13.7 Generalized Coordinate System.

13.8 Multibody Lagrangian Dynamics.


A Global Frame Triple Rotation.

B Local Frame Triple Rotation.

C Principal Central Screw Triple Combination.

D Industrial Link DH Matrices.

E Trigonometric Formula.


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Author Information

Reza N. Jazar is a professor of mechanical engineering, receiving his master's degree from Tehran Polytechnic in 1990, specializing in robotics. In 1997, he acquired his PhD from Sharif Institute of Technology in nonlinear dynamics and applied mathematics. Prof. Jazar is a specialist in classical and nonlinear dynamics, and has extensive experience in the field of dynamics and mathematical modeling. Prof. Jazar has worked in numerous universities worldwide, and through his years of work experience, he has formulated many theorems, innovative ideas, and discoveries in classical dynamics, robotics, control, and nonlinear vibrations. Razi Acceleration, Theory of Time Derivative, Order-Free Transformations, Caster Theory, Autodriver Algorithm, Floating-Time Method, Energy-Rate Method, and RMS Optimization Method are some of his discoveries and innovative ideas. Some of his recent discoveries in kinematics dynamics were introduced in Advanced Dynamics for the first time. Prof. Jazar has written over 200 scientific papers and technical reports and has authored more than thirty books including Theory of Applied Robotics: Kinematics, Dynamics, and Control, Second Edition and Vehicle Dynamics: Theory and Application.
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