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# Advanced Dynamics. Rigid Body, Multibody, and Aerospace Applications

• Published: April 2011
• Region: Global
• 1344 Pages
• John Wiley and Sons Ltd

According to the author and reviewers, more than 50% of the material taught in courses such as Advanced Dynamics, Mutibody Dynamics, and Spacecraft Dynamics is common to one another. Where graduate students in Mechanical and Aerospace Engineering may have the potential to work on projects that are related to any of the engineering disciplines, they have not been exposed to enough applications in both areas for them to use this information in the real world. This book bridges the gap between rigid body, multibody, and spacecraft dynamics for graduate students and specialists in mechanical and aerospace engineering. The engineers and graduate students who read this book will be able to apply their knowledge to a wide range of applications across different engineering disciplines.

The book begins with a review on coordinate systems and particle dynamics which will teach coordinate frames. The transformation and rotation theory along with the differentiation theory in different coordinate frames will provides the required background to learn the rigid body dynamics based on Newton-Euler principles. Applications to this coverage can be found in vehicle dynamics, spacecraft dynamics,

Preface.

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.

References.

A Global Frame Triple Rotation.

B Local Frame Triple Rotation.

C Principal Central Screw Triple Combination.

D Industrial Link DH Matrices.

E Trigonometric Formula.

Index.

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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