Advanced Dynamics

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.

Autorentext
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.

Zusammenfassung
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.

Inhalt
Preface xiii Part I Fundamentals 1 1 Fundamentals of Kinematics 3 1.1 Coordinate Frame and Position Vector 3 1.1.1 Triad 3 1.1.2 Coordinate Frame and Position Vector 4 1.1.3 Vector Definition 10 1.2 Vector Algebra 12 1.2.1 Vector Addition 12 1.2.2 Vector Multiplication 17 1.2.3 Index Notation 26 1.3 Orthogonal Coordinate Frames 31 1.3.1 Orthogonality Condition 31 1.3.2 Unit Vector 34 1.3.3 Direction of Unit Vectors 36 1.4 Differential Geometry 37 1.4.1 Space Curve 38 1.4.2 Surface and Plane 43 1.5 Motion Path Kinematics 46 1.5.1 Vector Function and Derivative 46 1.5.2 Velocity and Acceleration 51 1.5.3 Natural Coordinate Frame 54 1.6 Fields 77 1.6.1 Surface and Orthogonal Mesh 78 1.6.2 Scalar Field and Derivative 85 1.6.3 Vector Field and Derivative 92 Key Symbols 100 Exercises 103 2 Fundamentals of Dynamics 114 2.1 Laws of Motion 114 2.2 Equation of Motion 119 2.2.1 Force and Moment 120 2.2.2 Motion Equation 125 2.3 Special Solutions 131 2.3.1 Force Is a Function of Time, F = F (t) 132 2.3.2 Force Is a Function of Position, F = F(x) 141 2.3.3 Elliptic Functions 148 2.3.4 Force Is a Function of Velocity, F = F (v) 156 2.4 Spatial and Temporal Integrals 165 2.4.1 Spatial Integral: Work and Energy 165 2.4.2 Temporal Integral: Impulse and Momentum 176 2.5 Application of Dynamics 188 2.5.1 Modeling 189 2.5.2 Equations of Motion 197 2.5.3 Dynamic Behavior and Methods of Solution 200 2.5.4 Parameter Adjustment 220 Key Symbols 223 Exercises 226 Part II Geometric Kinematics 241 3 Coordinate Systems 243 3.1 Cartesian Coordinate System 243 3.2 Cylindrical Coordinate System 250 3.3 Spherical Coordinate System 263 3.4 Nonorthogonal Coordinate Frames 269 3.4.1 Reciprocal Base Vectors 269 3.4.2 Reciprocal Coordinate Frame 278 3.4.3 Inner and Outer Vector Product 285 3.4.4 Kinematics in Oblique Coordinate Frames 298 3.5 Curvilinear Coordinate System 300 3.5.1 Principal and Reciprocal Base Vectors 301 3.5.2 PrincipalReciprocal Transformation 311 3.5.3 Curvilinear Geometry 320 3.5.4 Curvilinear Kinematics 325 3.5.5 Kinematics in Curvilinear Coordinates 335 Key Symbols 346 Exercises 347 4 Rotation Kinematics 357 4.1 Rotation About Global Cartesian Axes 357 4.2 Successive Rotations About Global Axes 363 4.3 Global RollPitchYaw Angles 370 4.4 Rotation About Local Cartesian Axes 373 4.5 Successive Rotations About Local Axes 376 4.6 Euler Angles 379 4.7 Local RollPitchYaw Angles 391 4.8 Local versus Global Rotation 395 4.9 General Rotation 397 4.10 Active and Passive Rotations 409 4.11 Rotation of Rotated Body 411 Key Symbols 415 Exercises 416 5 Orientation Kinematics 422 5.1 AxisAngle Rotation 422 5.2 Euler Parameters 438 5.3 Quaternion 449 5.4 Spinors and Rotators 457 5.5 Problems in Representing Rotations 459 5.5.1 Rotation Matrix 460 5.5.2 AxisAngle 461 5.5.3 Euler Angles 462 5.5.4 Qu…

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