Advanced Dynamics
Rigid Body, Multibody, and Aerospace Applications
1. Edition April 2011
1344 Pages, Hardcover
Wiley & Sons Ltd
Short Description
Modern mechanical and aerospace systems are often very complex and consist of many rigid components interconnected by joints and force elements. This book bridges the gap between rigid body, multi-body, and spacecraft dynamics for graduate students and specialists in mechanical and aerospace engineering. Coverage of special applications highlight the different aspects of dynamics and provide understanding of advanced systems across all related disciplines. The author presents the material using his own theory of differentiation in different coordinate frames which allows for better understanding and application by students and professionals.
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, aircraft dynamics, robot dynamics, and multibody dynamics, each in a chapter. The Newton equations of motion will be transformed to Lagrange equation as a bridge to analytical dynamics. The methods of Lagrange and Hamilton will be applied on rigid body dynamics. Finally through the coverage of special applications this text provides understanding of advanced systems without restricting itself to a particular discipline. The author will provide a detailed solutions manual and powerpoint slides as ancillaries to this book.
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.
